formed by two chord
s. An inscribed angle's degree measure
is half that of its intercept
O, chord AB, radius
- 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).
Although this is a special case of this theorem (one of the chord
s is a diameter
), it can be used to demonstrate the theorem
's veracity in other circumstances.