Circles (Edexcel A-Level Mathematics): Quizzes

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Angle in a Semicircle
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What is the measure of any angle subtended by a diameter of a circle?

90∘90^\circ

What is another name for Thales' theorem?

Angle in a semicircle

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

90∘90^\circ

For Thales' theorem, which side of the triangle must be the diameter?

The side opposite the right angle

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, what is the relationship between ∠AOC\angle AOC and ∠ACB\angle ACB?

∠AOC=2×∠ACB\angle AOC = 2 \times \angle ACB

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

A right triangle

How can you verify that ∠ACB=90∘\angle ACB = 90^\circ in a triangle inscribed in a circle?

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

Given AB=10AB = 10 (diameter), AC=6AC = 6, BC=8BC = 8, what is 62+826^2 + 8^2?

100100

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

90∘90^\circ

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