91Ó°ÊÓ

Let \(\angle \mathrm{A}\) be inscribed in a circle, and let \(\mathrm{m} \angle \mathrm{A}<90^{\circ} .\) Let \(\angle \mathrm{P}\) be the angle, with vertex at the center of the circle, which intercepts the same arc as \(\angle \mathrm{A}\). (Then \(\angle \mathrm{A}\) and \(\angle \mathrm{P}\) are said to be related). Prove: \(\mathrm{m} \angle \mathrm{A}=(1 / 2) \mathrm{m} \angle \mathrm{P}\).

Prove that inscribed angles which intercept the same arc are congruent.

Given two intersecting chords of a circle, show that the measure of the angle formed by the intersection is one-half the sum of the measures of the arcs intercepted by the angle and its vertical angle.