Problem
GEO-B1-M07-P019 A Circle for Replacing an Angle
#19
★★★☆☆ Level 3 of 5
Points \(A,B,C,D\) lie on one circle. Prove that \(\angle ABC=\angle ADC\), if points \(B\) and \(D\) lie on the same side of chord \(AC\). Explain why drawing such a circle is useful in similar problems.
Both angles stand on chord \(AC\).
Angles \(\angle ABC\) and \(\angle ADC\) are inscribed and stand on the same chord \(AC\). Therefore they are equal. In similar problems, a circle is useful because it lets us replace one angle by another angle located in a more convenient part of the diagram.
This problem connects the toolbox with the main pattern from the circle module.