Circles questions | form three Basic Mathematics

Find the value of the angles a and b in the figure below

Prove that opposite angles ofa cyclic quadrilateral are supplementary.

Find the values of x, y and z in the figure below:

In the figure below, BC is a diameter of the circle, O is the centre of the circle and side CD of the cyclic
quadrilateral ABCD is produced to E.

1. With reasons, name the right angles in this figure.
2. Show that  =
3. If  and , find 

1. The value of 
2. The lengths AB and BD given that CB=10cm.

In the following figure; a regular hexagon is inscribed in a circle. If the perimeter of the hexagon is 42cm find;

1. The radius of the circle
2. The area of the circle and the regular polygon
3. The area of the shaded region 

In the following figure A, B, C and D lie on the circle; O is the centre of the circle , BD is its diameter and PAT is the tangent of the circle at A.

If , , find , , and .

In the figure below, BD is a tangent to the circle having the centre O.

Given that angle , find the values of angles marked X,Y and Z.

A bucket UVST was made from the cone URT such that its top radius is 12cm, bottom radius is 9cm and its depth (PQ) is 10cm.

1. Find the height QR of the cone VRS, using the fact that triangles PRT and QRS are similar.
2. Find the volume of the bucket, giving your answer in four significant figures.

In the diagram below PA and PB are tangents to the circle. If O is the centre of the circle, find the values of x and y.

In the figure below, TA and TB are tangents to the circle having centre O. Given that ATB =50°, find

1. angle ABT
2. angle OBA
3. angle ACB