Proof That a Triangle Drawn in a Semicircle is Right Angled

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If a triangle is drawn in a semicircle, with the diameter forming one side of the circle, as below, the angle formed opposite the diameter (angle) is a right angle.

The proof follows straight from the fact that the angle subtended by an arc at the centre of a circle is twice the angle subtended at the circumference, together with the fact that angleso 

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