Question

In the adjoining figure,if O is the cente of circumcircle of triangle ABC and angle AOC=110degree., Let us write by calculating , the value of angle ABC. ​

Answer 1

Since it is given that ∠AOC = 110° and by the theorem:-

The angle formed at the centre of a circle by an arc, is double of the angle formed by the same arc at any point on circle.

Since APCB forms a cyclic quadrilateral and we know that sum of opposite sides of a cyclic quadrilateral is equal to 180°

⇒ ∠APC + ∠ABC = 180

⇒ ∠ABC = 180 – 55 = 125°