In the given figure, ∠x = ∠y and PO = RO, then :

1. RB = AO

2. BO = PA

3. BP = AR

4. RB = OB

From figure,

OP is a straight line.

∴ ∠OAR + x = 180°

⇒ ∠OAR = 180° - x

OR is a straight line.

∴ ∠PBO + y = 180°

⇒ ∠PBO = 180° - y

Since, ∠x = ∠y

∴ ∠OAR = ∠PBO

In △ PBO and △ OAR,

⇒ PO = RO (Given)

⇒ ∠PBO = ∠OAR (Proved above)

⇒ ∠O = ∠O (Common angle)

∴ △ PBO ≅ △ OAR (By A.A.S. axiom)

We know that,

Corresponding parts of congruent triangles are equal.

∴ BP = AR.

Hence, Option 3 is the correct option.