Question

1. triangle abc is inscribed in circle o as shown. $overline{ac}$ is a diameter of circle o. which relationship must be true?

Explanation:

Step1: Recall circle - angle property

An angle inscribed in a semi - circle is a right angle. Since $\overline{AC}$ is a diameter of circle $O$ and $\angle ABC$ is an inscribed angle subtended by the diameter $\overline{AC}$, by the inscribed - angle theorem, $\angle ABC = 90^{\circ}$.

Answer:

$\angle ABC=90^{\circ}$