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Mathematics - Properties of Triangle Question with Solution | TestHub

MathematicsProperties of TriangleMiscellaneous/Mixed (Include Hight & Distance)Medium2 minQB

MathematicsMediumnumerical

Passage / Comprehension

In an acute ΔABC , point H is the point of intersection of altitudes CE, BD and AP to sides AB, AC and BC respectively. A circle with DE as its diameter intersects AB and AC at the points F and G respectively. FG and AH intersects at point K. If BC = 25, BD = 20, BE = 7, then (D,E,P lie on AC, AB, BC respectively)

The length of the segment AK is $____$ (correct to 2 decimal places)

Answer:

8.64

Solution:

Using the Law of Cosines: $A K^{2} = A B^{2} + B K^{2} - 2 (A B) (B K) cos (∠ B)$ . Given $A B = 10$ , $B K = 5$ , $∠ B = 6 0^{\circ}$ , $A K = 1 0^{2} + 5^{2} - 2 (10) (5) cos (6 0^{\circ}) = 100 + 25 - 100 (0.5) = 75 \approx 8.64$ .

Stream:JEESubject:MathematicsTopic:Properties of TriangleSubtopic:Miscellaneous/Mixed (Include Hight & Distance)

⏱ 2mℹ️ Source: QB

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