Circles (AQA A-Level Mathematics): Flashcards

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Angle in a Semicircle
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Other name for angle in semicircle theorem

Thales' theorem

Angle subtended by diameter of circle

90°90° (right angle)

△ABC\triangle ABC inscribed, ABAB diameter. ∠ACB=?\angle ACB = ?

90°90°

Thales' proof: OAOA, OBOB, OCOC relation (OO = centre)

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

∠AOC\angle AOC when ABAB is diameter

180°180°

∠AOC\angle AOC and ∠ACB\angle ACB relation (Thales)

∠AOC=2∠ACB\angle AOC = 2\angle ACB

Triangle in semicircle with diameter as side

Right triangle

AC=6AC=6, BC=8BC=8, AB=10AB=10 (diam). Verify right triangle

62+82=1026^2+8^2=10^2 ✓

Diameter PQPQ, RR on circle. ∠PRQ=?\angle PRQ = ?

90°90°

Thales' theorem statement

Angle subtended by diameter = 90°90°

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