Corollary 3 of Inscribed angle theorem
Include Formula
Corollary 3: The measure of an angle formed by two chords intersecting inside a circle is half the sum of the intercepted arcs.
Formula:
m∠AOD = (m∠ACB + m∠APB)/2
Where:
m∠AOD = Measure of the angle formed by two chords intersecting inside a circle
m∠ACB = Measure of an inscribed angle that intercepts arc AB
m∠APB = Measure of an inscribed angle that intercepts arc CD
Corollary 3 of the Inscribed Angle Theorem states that if two inscribed angles of a circle intercept the same arc, then these angles are congruent.
The formula for this corollary is:
∠AOC = ∠BOD
where:
- ∠AOC and ∠BOD are the two inscribed angles that intercept the same arc AB.
- A and B are points on the circle.
- O is the center of the circle.
This formula holds true whenever the two inscribed angles intercept the same arc on the circle.