Problem
GEO-B1-M08-P018 An Angle Bisector in a Circle
#18
★★★★☆ Level 4 of 5
In cyclic quadrilateral \(ABCD\), diagonal \(AC\) bisects angle \(BAD\). Prove that \(BC=CD\).
Equal inscribed angles stand on equal chords.
Since \(AC\) bisects \(\angle BAD\), \(\angle BAC=\angle CAD\). Angle \(\angle BAC\) stands on chord \(BC\), and \(\angle CAD\) stands on chord \(CD\). Equal inscribed angles stand on equal chords, hence \(BC=CD\).
Mixes an angle bisector, a circle, and equal chords.