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Theorem: Angle is a semi circle is a right angle. Given : Angle AOB is in semi circle. To prove: Angle ACB = 90^{o} Proof: Angle ACB = 1/2 angle AOB (angle subtended at the centre is twice angle at circumference) Angle AOB = 180^{o} (straight line) Hence ACB = 90^{o}
Theorem: Angles in the same segment of a circle are equal.
Directions: Solve the following 