Problem
GEO-B1-M05-P004 Equal Chords and Central Angles
#4
★☆☆☆☆ Level 1 of 5
In a circle with centre \(O\), chords \(AB\) and \(CD\) are equal. Prove that \(\angle AOB=\angle COD\).
Compare triangles \(AOB\) and \(COD\).
We have \(OA=OB=OC=OD\), since these are radii of one circle. By condition \(AB=CD\). Hence \(\triangle AOB\cong\triangle COD\) by SSS, so \(\angle AOB=\angle COD\).
Connects circle geometry with triangle congruence from Module 2.