In the figure given, RS is a diameter of the circle. NM is parallel to RS and ∠MRS = 29°.

Calculate :

(i) ∠RNM,

(ii) ∠NRM.

In the given figure, SP is the bisector of ∠RPT and PQRS is a cyclic quadrilateral. Prove that :

SQ = SR.

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.