Question

In the given figure, the centre O of the small circle lies on the circumference of the bigger circle. If $\angle$ APB = ${75}^o$ and $\angle$BCD = ${40}^o$, find :

(i) $\angle$ AOB,

(ii) $\angle$ ACB,

(iii) $\angle$ ABD,

(iv) $\angle$ ADB.

Answer 1

Join A and B as shown in the diagram.

(i) (angle subtended by an chord on the center is double that subtended by the same chord on the circumference)

(ii) ( is a cyclic quadrilateral)

(iii) ( is a cyclic quadrilateral)

(iv) ( is a cyclic quadrilateral)