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

Solution

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

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