Circles (AQA A-Level Mathematics): Quizzes

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Angle in a Semicircle
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What does Thales' theorem state about an angle subtended by a diameter?

It is a right angle

What is another name for the angle in a semicircle theorem?

Thales' theorem

If △ABC\triangle ABC is inscribed in a circle where ABAB is the diameter, what is ∠ACB\angle ACB?

90∘90^\circ

In the proof, if OO is the centre and CC is on the circle, what is true about OAOA, OBOB, OCOC?

OA=OB=OC=rOA = OB = OC = r

In the proof, if ∠AOC=180∘\angle AOC = 180^\circ, what equation relates this to ∠ACB\angle ACB?

2×∠ACB=180∘2 \times \angle ACB = 180^\circ

A triangle inscribed in a semicircle with one side as the diameter is always what type?

A right triangle

Given diameter AB=10AB = 10, AC=6AC = 6, BC=8BC = 8, what does 62+826^2 + 8^2 equal?

100100

To verify ∠ACB=90∘\angle ACB = 90^\circ, which condition should △ABC\triangle ABC satisfy?

AC2+BC2=AB2AC^2 + BC^2 = AB^2

If PQPQ is a diameter and RR is on the circumference forming △PRQ\triangle PRQ, what is ∠PRQ\angle PRQ?

90∘90^\circ

What is the measure in degrees of an angle subtended by a diameter according to Thales' theorem?

90∘90^\circ

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