Problem
GEO-B1-M05-P011 Two Points See a Segment Under a Right Angle
#11
★★☆☆☆ Level 2 of 5
In quadrilateral \(ABCD\), it is known that \(\angle ACB=90^\circ\) and \(\angle ADB=90^\circ\). Prove that points \(A,B,C,D\) lie on one circle.
Points \(C\) and \(D\) lie on the circle with diameter \(AB\).
If a point sees segment \(AB\) under a right angle, then it lies on the circle with diameter \(AB\). Since \(\angle ACB=90^\circ\) and \(\angle ADB=90^\circ\), both points \(C\) and \(D\) lie on this circle. Hence \(A,B,C,D\) lie on one circle.
One of the most common ways to prove cyclicity.