Thread: Angles in cyclic quadrilateral in semi-circle

Given a cyclic quadrilateral ABCD in a semi-circle, (let AD be the diameter),let AB=BC=1. Draw the line DB.
Prove that angle ADB= angle BDC

This was taken as obvious in a solution I read, but it is not at all obvious to me. Help in understanding this result would be appreciated.

Hello, I-Think!

Didn't they explain why it is "obvious"?


Angles and are inscribed angles.
. . They are measured by one-half their intercepted arcs.

We are told that chords and are equal.
. . Hence, their respective arcs are equal: .

Therefore: .