Two chords AB and CD of circle whose centre is O, meet at

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Two chords AB and CD of circle whose centre is O, meet at the point P and ∠ AOC = 50°, ∠ BOD = 40°. Then the value of ∠ BPD is

1. 60°
2. 40°
3. 45°
4. 75°

Correct Option: C

According to question , we draw a figure ofa circle with centre O and AB and CD are two chords

Here , ∠ AOC = 50°, ∠ BOD = 40°
Join CB.
∠AOC + ∠BOD = 2∠ABC + 2∠BCD (Exterior angles of triangle)
∠AOC + ∠BOD = 2(∠ABC + ∠BCD) = 2∠BPD

∴ ∠BPD =	1	(50° + 40°) = 45°
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