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Question
In the given figure, O is the centre of the circle. Find ∠CBD.
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Solution
It is given that, `angle AOC = 100°`
We have to find `angleCBD`
Since `angleAOC = 100°` (Given)
So,
`angleAPC = 1/2 angleAOC` (The angle subtended by an arc of a circle at the centre is double the angle subtended by it at any point on the remaining part of the circle.)
`⇒ angleAPC = 1/2 xx 100`
= 50°
Now,
`angle APC + angleABC = 180° ` (Opposite pair of angle of cyclic quadrilateral)
So,
`50°+ angleABC = 180° `
`angleABC = 180° - 50°`
= 130°
⇒`angle ABC` = 130° …… (1)
`angle ABC + angleCBD = 180° ` (Linear pair)
`130° + angle CBD = 180° ( angleABC = 130)`
`angle CBD = 180° - 130° `
= 50°
Hence `angle CBD ` = 50°
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