Problem
GEO-B1-M05-P009 Equal Chords, Equal Angles
#9
★★☆☆☆ Level 2 of 5
Points \(A,B,C,D\) lie on a circle. It is known that \(AB=AC\). Prove that \(\angle ADB=\angle ADC\).
The angles stand on equal chords \(AB\) and \(AC\).
Equal chords \(AB\) and \(AC\) cut off equal arcs. Angle \(\angle ADB\) stands on chord \(AB\), and angle \(\angle ADC\) stands on chord \(AC\). Therefore these inscribed angles are equal.
Practises the transition “equal chord → equal angle”.