In ∆ABC, a line XY parallel to BC cuts AB at X and AC at Y. If BY bisects ∠XYC, then
Question:

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

(a) $\mathrm{BC}=\mathrm{CY}$

(b) $B C=B Y$

(c) $B C \neq C Y$

(d) $B C \neq B Y$

Solution:

Given: XY||BC and BY is bisector of XYC.

Since XY||BC

So ∠YBC = ∠BYC     (Alternate angles)

Now, in triangle BYC two angles are equal. Therefore, the two corresponding sides will be equal.

Hence, BC = CY

Hence option (a) is correct.