Two chords AB and CD of a circle with centre O intersect

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Two chords AB and CD of a circle with centre O intersect at P. If ∠APC = 40°. Then the value of ∠AOC + ∠BOD is

1. 50°
2. 60°
3. 80°
4. 120°

Correct Option: C

According to question , we draw a figure of a circle with centre O ,

Given , ∠APC = 40°.
Arc AC subtends ∠AOC at the centre and ∠ABC at the circumference.
Similarly, ∠BOD = 2∠BCD
∴ ∠AOC + ∠BOD = 2 (∠ABC + ∠BCD)
∠AOC + ∠BOD = 2 ∠APC = 2 × 40° = 80°