CK12 - Geometry

We obtain

Since is a centralanglethat correspondsto then,.

This completesthe proof.

Example 1

Find the valuesof

and

.

First we find angle

Usingthe Measureof the TangentChordTheoremwe concludethat:

and

Therefore,

AnglesInsidea Circle

TheoremThe measureof the angleformedby two chordsthat intersectinsidea circleis equalto half the
sum of the measureof their interceptedarcs.In otherwords,the measureof the angleis the average(mean)
of the measuresof the interceptedarcs.