Question

In the given figure, O is the centre of the circle. Find ∠CBD.

Answer 1

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°