Paper 2 · Circle theorems
TB is a diameter of a circle, and chords TA, TC, TD are drawn such that angle ATB = angle BTC = angle CTD = 25°. Why must AB=BC=CD?
AAngles in the same segment are equal
BThe perpendicular from the centre bisects the chord
COpposite angles of a cyclic quadrilateral sum to 180°
DEqual angles at the circumference subtend equal chords
Explanation: Equal inscribed angles (25° each) subtend equal chords, so AB=BC=CD.
Derived from ZIMSEC Mathematics Paper 2, November 1999, Q3
