# ANGLE SUBTENDED BY AN ARC AT CENTER OF CIRCLE WORKSHEET

Work out the size of each angle marked with a letter. Give reasons for your answers.

Problem 1 :

Solution

Problem 2 :

Solution

Problem 3 :

P, Q and R are points on the circumference of a circle, center, O. Angle PRQ = 64˚. SP and SQ are tangents to the circle at the points P and Q respectively.

Work out the size of angle

i) PSQ      ii) PQO       iii) POS      iv) QSO

Problem 4 :

P, Q and R are points on the circumference of a circle, center, O. Angle PSQ = 60˚. SP and SQ are tangents to the circle at the points P and Q respectively.

a. Work out the size of angle

i) QPS      ii) PQO      iii) PRQ      iv) POQ

b. what type of triangle is PQS?

c. Given that angle OQR = 10, work out the size of angle OPR.

Solution

Problem 5 :

P, Q, R and S are points on the circumference of a circle, center, O. PT and TR are tangents to the circle. OST is a straight line.

Angle OTR = 38˚

Find the size of the angle:

i) ROT  ii) PQR  iii) SRT  iv) PSO  v) PST

Solution

1) a = 130˚, b = 65˚, c = 115˚

2) g = 127˚.

3)  PSQ = 52˚,  PQO = 26˚, POS = 64˚, QSO = 26˚

4) QPS = 60˚, PQO = 30˚, POQ = 120˚, PRQ = 60˚, Equilateral triangle, OPR = 50˚

5)  x = 52˚, PQR = 52˚, SRT = 26˚, PSO = RSO = 64˚, PST = 116˚

In each of the following figures, O is the center of the circle. Calculate the values of x and justify your answer.

Problem 1 :

Solution

Problem 2 :

Solution

Problem 3 :

Solution

Problem 4 :

Solution

Problem 5 :

Solution

Problem 6 :

Solution

Problem 7 :

P, Q and R are points on the circumference of a circle, center O. Angle PRQ = 64, SP and SQ are tangents to the circle at the points P and Q respectively. Work out the size of angle.

i) ∠PSQ     ii)  ∠POS        iii)  ∠QSO

Solution

1) x = 68

2) x = 73˚

3) x = 98˚

4)  x = 124˚

5)  x = 50˚

6)  x = 55˚

7)  i)  ∠PSQ = 52   ii)  ∠POS = 26   iii)  ∠QSO = 64

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