Consider a triangle and points and on side such that

MATHEMATICS · Subjective · ICSE · Mathematics · Geometry · Geometry

Problem

Consider a triangle

ABC

and points

A_1

and

B_1

on side

BC

such that

\angle BAA_1=\angle B_1AC

. If the incircles of triangles

BAA_1

and

B_1AC

touch sides

BA_1

and

B_1C

M

and

N

, respectively, prove that

\frac{1}{BM}+\frac{1}{MA_1}=\frac{1}{B_1N}+\frac{1}{NC}