In the figure, given below, P and Q are the centers of two circles intersecting at B and C. ACD is a straight line. Calculate the numerical value of x.

The figure shows two circles which intersect at A and B. The center of the smaller circle is O and lies on the circumference of the larger circle. Given ∠APB = a°.

Calculate, in terms of a°, the value of :

(i) obtuse ∠AOB,

(ii) ∠ACB,

(iii) ∠ADB.

Give reasons for your answers clearly.

ABCD is a cyclic quadrilateral in which AB is parallel to DC and AB is a diameter of the circle. Given ∠BED = 65°; calculate :

(i) ∠DAB,

(ii) ∠BDC.

In the given figure, AB is a diameter of the circle. Chord ED is parallel to AB and ∠EAB = 63°. Calculate :

(i) ∠EBA,

(ii) ∠BCD.