01 · ARC ANGLE THEOREM
Theorem 9.7 (Central Angle Theorem)
The angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle (∠AOB = 2 ∠ACB).
SEGMENT DEDUCTIONS
Deductions from Central Angle Theorem
1. Angles in the same segment are equal: ∠APB = ∠AQB.
2. Angle in a semicircle is a right angle (90°): If AB is diameter, ∠ACB = 90°.
02 · CYCLIC QUADRILATERALS
Theorem 9.10 (Cyclic Quadrilateral)
The sum of either pair of opposite angles of a cyclic quadrilateral is 180° (∠A + ∠C = 180° and ∠B + ∠D = 180°).