Last updated on Nov 05, 2026

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 $\triangle ABC$ is inscribed in a circle where $AB$ is the diameter, what is $\angle ACB$ ?

$90^\circ$

In the proof, if $O$ is the centre and $C$ is on the circle, what is true about $OA$ , $OB$ , $OC$ ?

$OA = OB = OC = r$

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

$2 \times \angle ACB = 180^\circ$

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

A right triangle

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

$100$

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

$AC^2 + BC^2 = AB^2$

If $PQ$ is a diameter and $R$ is on the circumference forming $\triangle PRQ$ , what is $\angle PRQ$ ?

$90^\circ$

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

$90^\circ$

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