#### Question

In the given figure, O is the centre of the circle. The tangents at B and D intersect each other at point P. If AB is parallel to CD and ∠ABC = 55°, find:

(i) ∠BOD (ii) ∠BPD

#### Solution

i)

`∠`BOD = 2 `∠`BCD

⇒ `∠`BOD = 2 × 55° = 110°

ii) Since, BPDO is cyclic quadrilateral, opposite angles are supplementary.

∴ `∠`BOD + `∠`BPD = 180°

⇒ `∠`BPD = 180° - 110° = 70°

Is there an error in this question or solution?

Solution In the Given Figure, O is the Centre of the Circle. the Tangents at B and D Intersect Each Other at Point P. If Ab is Parallel to Cd and ∠Abc = 55°, Find: (I) ∠Bod (Ii) ∠Bpd Concept: Cyclic Properties.