Circle Geometry Test

The line PQR is a tangent to a circle with centre O.

QS is the diameter of the circle.

T is a point on the circumference of the circle such that POT is a straight line.

The angle OPQ is 34^o

Calculate the size of angle TQR. [WRITE NUMBER ONLY e.g. 23]

ABCD is a cyclic quadrilateral and PA is a tangent to the circle at A.
Angle BAP = 20^o and the angle ADC = 62^o.

Find

(a) angle ABC

(b) angle BAC

[WRITE ANSWER IN THE FORM 23;89 without any spaces.]

In the diagram, O is the centre of the circle.
SAT is a tangent of the circle at A.
Angle BAC = 80^o and angle SAB = angle TAC.

Calculate

Calculate

(a) BOC
(b) OBC
(c) ABO
(d) ACO

[WRITE ANSWER IN THE FORM 23;89;18;95 putting no spaces.]

Calculate the size of angle TQR.

A, B and C are points on the circumference of a circle of centre O.

D is a point on BC such that AOD is a straight line.

Calculate angles x, y and z.

[WRITE ANSWER IN THE FORM “a23b89c87”, putting no spaces.]

AD is a diameter of a circle centre O.
B and C are points on the circumference such that DC is parallel to OB. The angle OAC = 64^o

(a) Calculate the size of angle ODC.
(b) Calculate the size of angle AOB.
(c) Calculate the size of angle ACB.
(d) Calculate the size of angle OBC.

[WRITE ANSWER IN THE FORM 23;89;45;97, putting no spaces.]