Problem
GEO-B1-M08-P014 A Cyclic Trapezoid
#14
★★★★☆ Level 4 of 5
Quadrilateral \(ABCD\) is cyclic, and \(AB\parallel CD\). Prove that \(AD=BC\).
Obtain equal inscribed angles standing on chords \(AD\) and \(BC\).
Since \(AB\parallel CD\), \(\angle ABD=\angle BDC\). In the cyclic quadrilateral, \(\angle BDC=\angle BAC\), because both angles stand on chord \(BC\). Hence \(\angle ABD=\angle BAC\). These angles stand on chords \(AD\) and \(BC\), so the chords are equal: \(AD=BC\).
Mixes parallelism and circle geometry.