Problem
GEO-B1-M05-P003 Angle on a Diameter
#3
★☆☆☆☆ Level 1 of 5
Segment \(AB\) is a diameter of a circle, and point \(C\) lies on the circle. Prove that \(AC\perp BC\).
Angle \(\angle ACB\) stands on a semicircle.
The central angle corresponding to diameter \(AB\) is \(180^\circ\). The inscribed angle \(\angle ACB\) standing on the same arc is \(90^\circ\). Therefore \(AC\perp BC\).
It is important that the student sees “diameter → right angle” immediately.