Problem
GEO-B1-M07-P008 Two Right Angles
#8
★★☆☆☆ Level 2 of 5
In quadrilateral \(ABCD\), it is known that \(\angle ACB=90^\circ\) and \(\angle ADB=90^\circ\). Prove that \(A,B,C,D\) lie on one circle.
Draw the circle with diameter \(AB\).
Draw the circle with diameter \(AB\). Since \(\angle ACB=90^\circ\), point \(C\) lies on this circle. Since \(\angle ADB=90^\circ\), point \(D\) also lies on this circle. Therefore \(A,B,C,D\) lie on one circle.
A classic application of an auxiliary circle.