Problem
GEO-B1-M08-P022 Hidden Cyclicity
#22
★★★★☆ Level 4 of 5
In triangle \(ABC\), points \(D\) and \(E\) lie on \(AB\) and \(AC\). It is known that \(\angle CDE=\angle CBE\). Prove that points \(B,C,D,E\) lie on one circle.
Both angles look at segment \(CE\).
Angles \(\angle CDE\) and \(\angle CBE\) stand on the same segment \(CE\). If two points \(D\) and \(B\) see segment \(CE\) under equal angles, then they lie on one circle with \(C\) and \(E\). Therefore \(B,C,D,E\) are cyclic.
A mixed problem on the converse circle criterion.