Problem
GEO-B1-M05-P001 Half of a Central Angle
#1
★☆☆☆☆ Level 1 of 5
Points \(A,B,C\) lie on a circle with centre \(O\). It is known that \(\angle AOB=96^\circ\). Find \(\angle ACB\), if both angles stand on the same arc \(AB\).
An inscribed angle is half the central angle standing on the same arc.
Angle \(\angle AOB\) is central, and \(\angle ACB\) is inscribed. They stand on the same arc \(AB\). Therefore \(\angle ACB=\frac{1}{2}\cdot96^\circ=48^\circ\).
A basic numerical check of the relation between central and inscribed angles.