in triangle ABC, a line XY parallel to BC cuts AB at X and AC at Y. if BY bisects angle XYC, then show that BC = CY.

Question

in triangle ABC, a line XY parallel to BC cuts AB at X and AC at
Y if BY bisects angle XYC, then show that BC = CY

Tushar Kohli · Accepted Answer

Since

we will have

(alternate interior angles) But

(Given BY is bisects angle XYC) Hence comparing the above two relations we get

Hence, in triangle BYC, BC = CY