Problem
GEO-B2-M08-P013 Four Points via Sum of Angles
#13
★★★☆☆ Level 3 of 5
Prove that if \(\angle AXB+\angle AYB=180^\circ\), then points \(A,X,B,Y\) lie on one circle.
This is the second standard cyclicity criterion.
If the sum of opposite angles of quadrilateral \(AXBY\) is \(180^\circ\), then the quadrilateral is cyclic. Therefore points \(A,X,B,Y\) lie on one circle.
This criterion is often more convenient than equal angles.