Mathematics - Properties of Triangle Question with Solution | TestHub

MathematicsProperties of TriangleLength of angle bisector and median / Dist. between sp. PointsMedium2 minQB

MathematicsMediumsingle choice

In triangle ABC, D is the midpoint of BC and AD⊥AC. Find cos A cos C.

Options:

Answer:

Solution:

From CD=a/2 and AD⊥AC, cos C=AC/CD=2b/a. The cosine rule at C gives ( $a^{2}$ + $b^{2}$ - $c^{2}$ )/(2ab)=2b/a, so $a^{2}$ - $c^{2}$ = $3 b^{2}$ . At A, cos A=( $b^{2}$ + $c^{2}$ - $a^{2}$ )/(2bc)=-b/c. Hence cos A cos C=- $2 b^{2}$ /(ac)=2( $c^{2}$ - $a^{2}$ )/(3ac).

Stream:JEESubject:MathematicsTopic:Properties of TriangleSubtopic:Length of angle bisector and median / Dist. between sp. Points

⏱ 2mℹ️ Source: QB

Doubts & Discussion

Loading discussions...