The angle in a semicircle is a right angle.
Proof:
Directly from Theorem as ∠AOC=180°
The angle subtended by an arc at the centre of a circle is twice the angle subtended at any point on the circumference.
∠ABC=\(\frac{1}{2}\)∠AOC=\(\frac{1}{2}\)×180°=90°
Alternate Proof:
Join OB, ∠AOB = 180°− 2∠A; ∠COB = 180°−2∠C;
∠AOB + ∠COB = 180°− 2∠A + 180°− 2∠C
180° = 360° − 2∠A − 2∠C
2∠ + 2∠ = 180° ⇒ ∠ + ∠ = 90°
∠B = 180° − (∠A + ∠C) = 180° − 90° = 90°
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