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Question
In following fig., O is the centre of the circle. Find ∠ CBD.
Solution
It is given that ∠ AOC = 100°
Arc AC subtends ∠ AOC at the centre of circle and ∠ APC on the circumference of the circle
∴ ∠ AOC = 2 c
⇒ ∠ APC = `(100°)/2` = 50°
It can be seen that APCB is a cyclic quadriIateral.
∴ ∠ APC + ∠ ABC = 180° (Sum of opposite angles of a cyclic quadrilateral)
⇒ ∠ ABC = 180° - 50° = 130°
Now , ∠ ABC + ∠ CBD = 180° (Linear pair angles)
∠ CBD = 180° - 130° = 50°
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