Mathematics › Properties of Triangle
Properties of Triangle Questions
216 questions across 7 subtopics — with step-by-step solutions.
Ambiguous case of triangle(8)
- In a triangle ABC, if a=2\sqrt{3} , b=6 an... | Mathematics | TestHub
- In a \triangle ABC , if a=6 , b=8 and \ang... | Mathematics | TestHub
- For a triangle with given sides a, b and a... | Mathematics | TestHub
- Let ABC and A B C^{1} be two non congruent... | Mathematics | TestHub
- If A=30^{\circ}, a=7 and \mathrm{b}=8 in \... | Mathematics | TestHub
- In triangle \mathrm{ABC} a=\sqrt{5} ; b=2... | Mathematics | TestHub
- In a \triangle A B C sides b, c \angle C a... | Mathematics | TestHub
- There exists a triangle ABC satisfying the... | Mathematics | TestHub
General (basic formula based)(71)
- In a triangle ABC , if r_a + r_b + r_c = 9... | Mathematics | TestHub
- In a triangle ABC , if a \cos A + b \cos B... | Mathematics | TestHub
- In a triangle ABC , if the angles A, B, C... | Mathematics | TestHub
- In a \triangle ABC , if a \cos A + b \cos... | Mathematics | TestHub
- In a triangle ABC , if r_a r_b = r r_c , w... | Mathematics | TestHub
- In a triangle ABC , if a^2+b^2+c^2 = 8R^2... | Mathematics | TestHub
- In a \triangle ABC , if (a+b+c)(a+b-c) = 3... | Mathematics | TestHub
- In a triangle ABC, if a=5 , b=7 , c=8 , th... | Mathematics | TestHub
- In a triangle ABC , the sides are a=3 , b=... | Mathematics | TestHub
- In a triangle ABC, if \angle A = 45^\circ... | Mathematics | TestHub
- In a triangle ABC , if A=30^{\circ} , B=60... | Mathematics | TestHub
- In a \triangle ABC , if the angles A, B, C... | Mathematics | TestHub
- In a triangle A B C with sides a, b and c,... | Mathematics | TestHub
- In triangle ABC, find cot(A/2)+cot(B/2)+co... | Mathematics | TestHub
- If the inradius of an equilateral triangle... | Mathematics | TestHub
- Match the progression statements.List ILis... | Mathematics | TestHub
- Statement I: Among triangles of fixed peri... | Mathematics | TestHub
- In triangle ABC, =/6. If sides opposite A,... | Mathematics | TestHub
- If in a triangle \mathrm{ABC}, b \cos ^{2}... | Mathematics | TestHub
- In a triangle, the lengths of the two larg... | Mathematics | TestHub
- The angles of a \triangle A B C satisfy. \... | Mathematics | TestHub
- In \triangle \mathrm{ABC} if \angle \mathr... | Mathematics | TestHub
- A triangle with integer side lengths has p... | Mathematics | TestHub
- In an equilateral triangle whose inradius... | Mathematics | TestHub
- Tangents at P,Q,R on a circle of radius r... | Mathematics | TestHub
- In \triangle \mathrm{ABC} if \cos \mathrm{... | Mathematics | TestHub
- In triangle ABC, a:b:c=(1+x):1:(1-x), x∈(0... | Mathematics | TestHub
- Match each expression with a value.List IL... | Mathematics | TestHub
- In triangle ABC, A=30° and b/c=(2++-1)/(2+... | Mathematics | TestHub
- In a \triangle A B C, a=5, b=4 and \tan \f... | Mathematics | TestHub
- An isosceles triangle has sides 2,2,x. Whi... | Mathematics | TestHub
- Match each expression in List I with its v... | Mathematics | TestHub
- In triangle ABC, cos A+sin A-2/(cos B+sin... | Mathematics | TestHub
- In a \triangle \mathrm{ABC}, \mathrm{a}, \... | Mathematics | TestHub
- If a:b:c=7:8:9, find cos A:cos B. | Mathematics | TestHub
- In triangle ABC, cot A=, cot B=, cot C=. W... | Mathematics | TestHub
- If the area of triangle ABC is -(c-a)², fi... | Mathematics | TestHub
- Positive x,y,z satisfy ++=25, +=9, and +xz... | Mathematics | TestHub
- Let a, b, c be the side lengths of triangl... | Mathematics | TestHub
- In \triangle A B C .3 a=b+c then \cot \mat... | Mathematics | TestHub
- Let x=a cos A, y=b cos B, z=c cos C in tri... | Mathematics | TestHub
- In triangle ABC, A=2/3, b-c=3 cm, and =9/2... | Mathematics | TestHub
- In triangle ABC, (a+b+c)(b+c-a)=. Which in... | Mathematics | TestHub
- In a \triangle A B C , the angles A, B, C... | Mathematics | TestHub
- If cot(A/2)=(b+c)/a, classify triangle ABC. | Mathematics | TestHub
- If /2<C<, in what interval does (+)/ lie? | Mathematics | TestHub
- If sin(A-B)=3/5, a/b=2 and A-B<90°, match... | Mathematics | TestHub
- Sides of a triangle inscribed in a circle... | Mathematics | TestHub
- If p_{1}, p_{2} and p_{3} are the altitude... | Mathematics | TestHub
- Match each condition to the triangle class... | Mathematics | TestHub
- If b +a =3c/2, find the minimum of (a+c)/(... | Mathematics | TestHub
- Which data do NOT uniquely determine an ac... | Mathematics | TestHub
- If a,b,c are sides of a triangle, find the... | Mathematics | TestHub
- If cos A+cos B+2cos C=2 in triangle ABC, w... | Mathematics | TestHub
- In acute triangle ABC, AD⊥BC and DE⊥AB. Ma... | Mathematics | TestHub
- The triangle O A B has O=(0,0), A=(2,0), B... | Mathematics | TestHub
- If the sides a, b, c of a \triangle A B C... | Mathematics | TestHub
- In triangle ABC, +=. Find (cot A+cot C)/co... | Mathematics | TestHub
- Match each classification. “Is” asks for a... | Mathematics | TestHub
- ABCD is a quadrilateral circumscribed abou... | Mathematics | TestHub
- If =+ and 2s=a+b+c, find 4s(s-a)(s-b)(s-c). | Mathematics | TestHub
- In an isosceles triangle ABC with AB=AC an... | Mathematics | TestHub
- In a triangle ABC , the foot of the perpen... | Mathematics | TestHub
- Statement 1: If a,b,c are the sides of a t... | Mathematics | TestHub
- Match the following quantities.List IList... | Mathematics | TestHub
- A circle of radius 4 cm is inscribed in \t... | Mathematics | TestHub
- In an isosceles triangle A B C with \angle... | Mathematics | TestHub
- Let ABC be a triangle with altitudes \math... | Mathematics | TestHub
- Find a cos(B-C)+b cos(C-A)+c cos(A-B) in t... | Mathematics | TestHub
- In triangle ABC, R(b+c)=a. Classify the tr... | Mathematics | TestHub
- Let the lengths of the altitudes drawn fro... | Mathematics | TestHub
Length of angle bisector and median / Dist. between sp. Points(37)
- In a \triangle ABC , if m_a, m_b, m_c are... | Mathematics | TestHub
- In a triangle ABC , if the sides are a=5 ,... | Mathematics | TestHub
- In a triangle ABC, if a=3 , b=4 , c=5 , fi... | Mathematics | TestHub
- In a \triangle ABC , if a=7, b=8, c=9 , fi... | Mathematics | TestHub
- In a triangle ABC, if a=6 , b=8 , c=10 , f... | Mathematics | TestHub
- In triangle ABC, A=2/3, AB=x, and AB·AC=1.... | Mathematics | TestHub
- If length of the side BC of a \triangle \m... | Mathematics | TestHub
- In triangle ABC, AB=1 cm and AC=2 cm. Exte... | Mathematics | TestHub
- In triangle ABC, medians AD and BE are dra... | Mathematics | TestHub
- Let \mathrm{AD}, \mathrm{BE}, \mathrm{CF}... | Mathematics | TestHub
- In a scalene triangle ABC, D is on AB with... | Mathematics | TestHub
- If in \triangle \mathrm{ABC} , circle with... | Mathematics | TestHub
- If ,, are the medians through A,B,C of tri... | Mathematics | TestHub
- In a triangle ABC with usual notations, th... | Mathematics | TestHub
- Triangle ABC has perpendicular medians AD... | Mathematics | TestHub
- In triangle ABC, the bisector of angle A m... | Mathematics | TestHub
- If ' l ' is the median from the vertex A t... | Mathematics | TestHub
- The sum of the squares of the sides of a t... | Mathematics | TestHub
- In a triangle \mathrm{ABC}, \mathrm{CH} an... | Mathematics | TestHub
- AD is a median of triangle ABC. AE and AF... | Mathematics | TestHub
- If the median A D of triangle A B C makes... | Mathematics | TestHub
- In \triangle A B C, B C=3 , and D lies on... | Mathematics | TestHub
- If A D and A D^{\prime} are the internal a... | Mathematics | TestHub
- In a triangle ABC , length of the bisector... | Mathematics | TestHub
- The ratios of the lengths of the sides B C... | Mathematics | TestHub
- T1 is isosceles with circumcircle K. T2 is... | Mathematics | TestHub
- If B=60^{\circ}, C=45^{\circ} and D divide... | Mathematics | TestHub
- The triangle ABC has \angle \mathrm{A}=60^... | Mathematics | TestHub
- If the bisector of A in triangle ABC makes... | Mathematics | TestHub
- Points D, E are taken on the side B C of a... | Mathematics | TestHub
- In triangle ABC, medians AD and CE meet at... | Mathematics | TestHub
- In triangle ABC, D is the midpoint of BC a... | Mathematics | TestHub
- There is a point P inside triangle ABC suc... | Mathematics | TestHub
- P lies on the altitude AD of triangle ABC,... | Mathematics | TestHub
- In triangle ABC, medians from B and C are... | Mathematics | TestHub
- In \triangle A B C, A B is vertical, B C h... | Mathematics | TestHub
- A circle of diameter 2x has its center on... | Mathematics | TestHub
Miscellaneous/Mixed (Include Hight & Distance)(15)
- In a \triangle ABC , if a^2, b^2, c^2 are... | Mathematics | TestHub
- In a triangle ABC, the sides are a=13 , b=... | Mathematics | TestHub
- In a \triangle ABC , if \cot A + \cot B +... | Mathematics | TestHub
- A ladder of length 10 \text{ m} leans agai... | Mathematics | TestHub
- In a \triangle ABC , if h_a, h_b, h_c are... | Mathematics | TestHub
- In a triangle ABC , if side b=8 , side c=1... | Mathematics | TestHub
- In triangle ABC if 2 a^{2} b^{2}+2 b^{2} c... | Mathematics | TestHub
- Given an isosceles triangle with equal sid... | Mathematics | TestHub
- The length of the segment AK is \_\_\_\_ (... | Mathematics | TestHub
- AP is equal to | Mathematics | TestHub
- The area of a cyclic Quadrilateral A B C D... | Mathematics | TestHub
- Find the point inside a \Delta from which... | Mathematics | TestHub
- If a, b, c are sides of a triangle satisfy... | Mathematics | TestHub
- Given a parallelogram whose acute angle is... | Mathematics | TestHub
- A circle is inscribed in a right trapezium... | Mathematics | TestHub
Orthocentre, pedal triangle based(17)
- In an acute-angled triangle ABC, if H is t... | Mathematics | TestHub
- The orthocentre of the triangle with verti... | Mathematics | TestHub
- In a \triangle ABC , if H is the orthocent... | Mathematics | TestHub
- In an acute-angled \triangle ABC , if O is... | Mathematics | TestHub
- In a \triangle A B C , perpendiculars are... | Mathematics | TestHub
- If a triangle has sides 3,4,5 cm, find the... | Mathematics | TestHub
- ABC is an acute angle triangle, \angle \ma... | Mathematics | TestHub
- In an acute-angled triangle ABC, let f,g,h... | Mathematics | TestHub
- In acute triangle ABC with orthocenter H,... | Mathematics | TestHub
- If x,y,z are distances of vertices A,B,C f... | Mathematics | TestHub
- If the orthocenter of an isosceles triangl... | Mathematics | TestHub
- In acute triangle ABC, O is the circumcent... | Mathematics | TestHub
- H is the orthocenter of an acute triangle... | Mathematics | TestHub
- Match the following. Parent triangles are... | Mathematics | TestHub
- Three lines 2 x+3 y-1=0, x+2 y-1=0 , and a... | Mathematics | TestHub
- The altitudes of a triangle lie on x+5 y-3... | Mathematics | TestHub
- In triangle ABC, A=30° and BC=2+. Find dis... | Mathematics | TestHub
Regular Polygon(6)
- The area of a regular hexagon inscribed in... | Mathematics | TestHub
- A regular hexagon is inscribed in a circle... | Mathematics | TestHub
- A regular polygon has n sides. If the rati... | Mathematics | TestHub
- A circle is inscribed in an equilateral tr... | Mathematics | TestHub
- S1 and S2 are areas of regular inscribed a... | Mathematics | TestHub
- If r and R are respectively the radii of t... | Mathematics | TestHub
r1,r–R formula based(62)
- In a \triangle ABC , if r_1, r_2, r_3 are... | Mathematics | TestHub
- In a triangle ABC , if R is the circumradi... | Mathematics | TestHub
- In a triangle ABC, if r_1, r_2, r_3 are th... | Mathematics | TestHub
- In a right-angled triangle ABC with the ri... | Mathematics | TestHub
- In a \triangle ABC , if R is the circumrad... | Mathematics | TestHub
- In a \triangle ABC , if r_1 = r + r_2 + r_... | Mathematics | TestHub
- In a triangle ABC, if r is the inradius an... | Mathematics | TestHub
- In \triangle \mathrm{ABC} if \angle C=90^{... | Mathematics | TestHub
- In triangle ABC, find (r_1+r_3)/(1+cos B). | Mathematics | TestHub
- An incircle of radius 4 touches BC, CA, AB... | Mathematics | TestHub
- A maximum-area right triangle is inscribed... | Mathematics | TestHub
- In a right-angled triangle ABC with A=/2 a... | Mathematics | TestHub
- In triangle ABC, C=60° and R=16. Find II_3... | Mathematics | TestHub
- Match the expressions.List IList II(A) If... | Mathematics | TestHub
- If a right angled \triangle A B C of maxim... | Mathematics | TestHub
- In triangle ABC, A-B=120° and R=8r. Find c... | Mathematics | TestHub
- In a triangle, r=r_1=2r_2=3r_3. Find a/b+b... | Mathematics | TestHub
- In triangle ABC, the incenter and circumce... | Mathematics | TestHub
- If a triangle has sides 3,4,5 cm, find the... | Mathematics | TestHub
- In triangle ABC, A-B=120° and R=8r. Find (... | Mathematics | TestHub
- In triangle ABC, A=/3 and inradius is 6 un... | Mathematics | TestHub
- The in-circle of \triangle A B C touches s... | Mathematics | TestHub
- With usual notation in triangle ABC , the... | Mathematics | TestHub
- In triangle ABC, (r_2-r_1)(r_3-r_1)=2r_2r_... | Mathematics | TestHub
- In triangle ABC, 2a = p(1/r_2+1/r_3)+q(1/r... | Mathematics | TestHub
- Consider a triangle ABC and let \mathrm{a}... | Mathematics | TestHub
- In triangle ABC, r=1, r_1=7, and R=3, with... | Mathematics | TestHub
- If the exradii r_1:r_2:r_3 are 1:2:3, find... | Mathematics | TestHub
- The lengths of the tangents drawn from the... | Mathematics | TestHub
- The perimeter of triangle ABC is 6 times t... | Mathematics | TestHub
- If the exradii of triangle ABC are r_1=8,... | Mathematics | TestHub
- Triangle A B C is right - angled at point... | Mathematics | TestHub
- In acute triangle ABC, r+=+ and B>/3. Whic... | Mathematics | TestHub
- If r_1,r_2,r_3 are the exradii of a triang... | Mathematics | TestHub
- In triangle ABC, match each expression wit... | Mathematics | TestHub
- In \triangle A B C , if r_{1}=6, R=5, r=2... | Mathematics | TestHub
- In triangle ABC, sin(A/2)=6/5 and II_i=9,... | Mathematics | TestHub
- The radii \mathrm{r}_{1}, \mathrm{r}_{2},... | Mathematics | TestHub
- If I be the incentre of triangle ABC and \... | Mathematics | TestHub
- In triangle ABC, I is the incenter. Find I... | Mathematics | TestHub
- In \triangle \mathrm{ABC}, \frac{\mathrm{r... | Mathematics | TestHub
- The exradii of triangle ABC are r_a,r_b,r_... | Mathematics | TestHub
- Let I be the incenter of triangle ABC, whe... | Mathematics | TestHub
- Given r=2, =4, s=12 and a<b<c, match the q... | Mathematics | TestHub
- If r=1, R=5, =10 in triangle ABC, find ab+... | Mathematics | TestHub
- Given r=2, =4, s=12 and a<b<c, match the q... | Mathematics | TestHub
- Quadrilateral ABCD is cyclic and tangentia... | Mathematics | TestHub
- For triangle ABC, (s-a)/=1/8, (s-b)/=1/12,... | Mathematics | TestHub
- In \triangle A B C \frac{\left(r_{1}+r_{2}... | Mathematics | TestHub
- If b+c=3a in triangle ABC, find cot(B/2)co... | Mathematics | TestHub
- If the circumcentre of triangle ABC lies o... | Mathematics | TestHub
- In triangle ABC, (s-r_2)/r_2=, where r_2 i... | Mathematics | TestHub
- In triangle ABC, r=2, B=60° and C=90°. Fin... | Mathematics | TestHub
- The in-circle of \triangle A B C touches s... | Mathematics | TestHub
- In triangle ABC, r_1=3, r_2=10, r_3=15. Fi... | Mathematics | TestHub
- In triangle ABC, match each expression wit... | Mathematics | TestHub
- In \triangle \mathrm{ABC} , if R(a+b)=c \s... | Mathematics | TestHub
- In triangle ABC, r=1, R=4, and =8. Find ab... | Mathematics | TestHub
- An incircle touches BC,CA,AB at D,E,F. BD,... | Mathematics | TestHub
- In triangle ABC, if B=90°, find arccos[R/(... | Mathematics | TestHub
- If in a triangle \mathrm{ABC}, \cos \mathr... | Mathematics | TestHub
- In triangle ABC, a:b:c=4:5:6. Find the rat... | Mathematics | TestHub
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