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

Given that angle OEC = 28°, find the values of angles marked X , Y and Z .

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

A chord is 6cm from the center of a circle with radius 10cm. What is the length of a chord?

Find the value of angle X in the figure below.

Find the angle x in the figure below

Prove that the sizes of the angles in the same segment of a circle are equal.

In the figure below, O is the centre of the circle and AD bisects angle BAC . Find angle BCD.

If O is the centre of a circle given below, find the value of x.

Below is a circle with centre 0 and radius r units. By considering the circumference of the circle, the area of the circle, the given angle 0 and the degree measures of a circle (360⁰), develop the formula for finding:

1. arc length AB
2. area of sector AOB.

(b) Find (i) the length of arc AB

(ii) the area of the sector

If ?=57⁰ and r=5.4cm (Use ? =22/7)

Find the central angle (in degrees) made by an arc of length 22cm in a circle whose radius is 63cm. Use .

In the following figure, prove that angles x and y are supplementary given that a and b are the angles at the centre of the circle.

In the following figure, AC=8cm, BE=3cm and CE=4cm. find length of DE 

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 angle ABD = 59 , CDB = 35, find ACD, ADB, DAT and CAO.

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.

(a)  With reasons, name the right angles in this figure.

(b) Show that Angle ADE = Angle ABC.

(c) If Angle ADE = 60 and Angle CAD = 25, find:

(i) the value of Angle ABD ,

(ii) the lengths AB and BD given that CB = 10cm.