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, the bisector of angle A meets side BC at D and the circumcircle again at E. Find DE.

Options:

Answer:

Solution:

By the angle-bisector theorem, BD=ac/(b+c), DC=ab/(b+c). The internal bisector length is AD=2bc cos(A/2)/(b+c). Intersecting chords give AD·DE=BD·DC, hence DE=[ $a^{2}$ bc/(b+c)²]/[2bc cos(A/2)/(b+c)]= $a^{2}$ sec(A/2)/[2(b+c)].

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

⏱ 2mℹ️ Source: QB

Doubts & Discussion

Loading discussions...