Problem
GEO-B1-M07-P003 Circle With a Diameter
#3
★☆☆☆☆ Level 1 of 5
Point \(C\) is such that \(\angle ACB=90^\circ\). Prove that \(C\) lies on the circle with diameter \(AB\).
Recall the converse of the theorem about an angle standing on a diameter.
The set of points from which segment \(AB\) is seen under a right angle is the circle with diameter \(AB\). Since \(\angle ACB=90^\circ\), point \(C\) lies on this circle.
A basic tool for problems with altitudes and right angles.