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Lines, Triangles and Circles · Question 58 of 67

Question 58

MediumOriginal question

O is the centre of a circle, and P and Q are points on it with ∠POQ=124∘\angle POQ = 124^\circ (the angle at the centre facing the minor arc PQ). R is a point on the minor arc PQ. What is ∠PRQ\angle PRQ?

Options for question 58

Show the answer and explanation
CorrectNot quiteAnswer D

Correct answer: D

Explanation

  1. Since R is on the minor arc, ∠PRQ\angle PRQ stands on the MAJOR arc PQ.

  2. The angle at the centre on the major arc is 360∘−124∘=236∘360^\circ - 124^\circ = 236^\circ.

  3. ∠PRQ=236∘÷2=118∘\angle PRQ = 236^\circ \div 2 = 118^\circ.

Worth noting

62° is the angle at a point on the MAJOR arc. The two answers always add to 180° because P, R, Q and a point on the major arc form a cyclic quadrilateral.

Concept
Angle at the centre is twice the angle at the circumference
Typical time
70 s
Your time
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The rule this testsCircles
Practise this chapter →

Ten questions from Lines, Triangles and Circles, at your own pace.

Practise this chapter →

Ten questions from Lines, Triangles and Circles, at your own pace.