Mathematics - Properties of Triangles Question with Solution | TestHub

MathematicsProperties of TrianglesGeneralMedium2 minPYQ_2019

MathematicsMediumsingle choice

Let $A B C$ be an acute-angled triangle and let $D$ be the mid-point of $B C$ . If $A B = A D$ , then $\frac{\tan B}{\tan C}$ equal

Answer:

Solution:

In $∆ A B C, D$ be the mid-point of $B C$ and $A B = A D \Rightarrow Δ A B D$ is isosceles.

Let $A M$ be the perpendicular drawn from $A$ to $B C$ .

$∴ A M$ is perpendicular bisector of $B D$

$B M = M D$

$\ln Δ A B M, \tan B = \frac{A M}{B M}$

$\ln Δ A M C, \tan C = \frac{A M}{C M}$

$∴ \frac{\tan B}{\tan C} = \frac{C M}{B M} = \frac{3 B M}{B M} = 3 [∵ C M = D M + C D]$

Stream:BITSATSubject:MathematicsTopic:Properties of TrianglesSubtopic:General

⏱ 2mℹ️ Source: PYQ_2019

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