Question

In ABC, a line XY parallel to BC cuts AB at X and AC at Y . If BY bisects $\angle XYC$ , then

• A. BC = CY
• B. BC = BY
• C. BC CY
• D. BC = XY

Answer 1

The correct option is A BC = CY

As $XY||BC$

$\angle XYB=\angle CBY-\left(1\right)$ (..... Alternate interior angles)

Sinc $BY$ bisects $\angle XYC$

$⟹\angle XYB=\angle CYB$

eqs.(1) $⟹\angle CBY=\angle CYB$

$BC=CY$ ( side opposite to equal angles are equal)