An

angle formed by two

chords. An inscribed angle's

degree measure is half that of its

intercepted

arc.

Proof:

Givens:

circle O, chord AB,

radius AO,

diameter BC.

- Angle BAO + angle ABC = angle AOC (by remote interior angles)
- AO = BO (both are radii)
- Triangle ABO is isosceles (definition of isosceles)
- Angle ABO = angle ABC (base angles of isosceles triangle are congruent)
- 2(angle ABC) = angle AOC (by substitution)
- Arc AC = angle AOC (definition central angle)
- 2(angle ABC) = arc AC (by substitution)
- Angle ABC = (arc AC)/2 (by division).

Q.E.D.Although this is a special case of this theorem (one of the

chords is a

diameter), it can be used to demonstrate the

theorem's veracity in other circumstances.