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High School Mathematics - 2
Theorems - Circles

Theorem: Angle is a semi circle is a right angle.

Given : Angle AOB is in semi circle.
To prove: Angle ACB = 90o
Proof: Angle ACB = 1/2 angle AOB (angle subtended at the centre is twice angle at circumference)
Angle AOB = 180o (straight line) Hence ACB = 90o

Theorem: Angles in the same segment of a circle are equal.

Directions: Solve the following