CK12 - Geometry

and both intercept is a centralangleand angle is an inscribed
angle.

We draw the diameterof the circlethroughpoints and , and let and

We see that is isoscelesbecause and are radii of the circleand are thereforecongruent.

Fromthis we can concludethat

Similarly, we can concludethat

We use the propertythat the sum of anglesinsidea triangleequals to find that:

and.

Then,

and

Therefore

.

InscribedAngleCorollariesa-d

The theoremabovehas severalcorollaries,whichwill be left to the studentto prove.

a. Inscribedanglesinterceptingthe samearc are congruent

b. Oppositeanglesof an inscribedquadrilateralare supplementary

c. An angleinscribedin a semicircleis a right angle

d. An inscribedright angleinterceptsa semicircle

Hereare someexamplesthe makeuse of the theoremspresentedin this section.

Example 1

Find the anglemarked

in the circle.