The measure of an inscribed angle is always half the measure of the arc it intercepts. You will prove and then use this theorem in the problems below.
Proving the Inscribed Angle Theorem
This proves that when an inscribed angle passes through the center of a circle, its measure is half the measure of the arc it intercepts.
This proves in general that the measure of an inscribed angle is half the measure of its intercepted arc.
Now let's find the measure of an angle.
In general, if a triangle is inscribed in a semicircle then it is a right triangle.
In #2-#3, you will use the circle below to prove that when two chords intersect inside a circle, the products of their segments are equal.
1. How are central angles and inscribed angles related?
To see the Review answers, open this PDF file and look for section 8.4.