Problem
GEO-B1-M05-P017 Equal Chords in an Angle Proof
#17
★★★☆☆ Level 3 of 5
Points \(A,B,C,D\) lie on one circle, and \(AB=CD\). Prove that \(\angle ADB=\angle CAD\).
Angle \(\angle ADB\) stands on chord \(AB\), while \(\angle CAD\) stands on chord \(CD\).
Equal chords \(AB\) and \(CD\) cut off equal arcs. Inscribed angles standing on equal arcs are equal. Therefore \(\angle ADB=\angle CAD\).
This problem looks simple, but it trains precise reading of chords.