Given: ∠AOB is a central angle and ∠ACB is a circumscribed angle. Prove: △ACO ≅ △BCO
Circle O is shown. Line segments A O and B O are radii. Tangents C B and C B intersect at point C outside of the circle. A line is drawn to connect points C and O.
We are given that angle AOB is a central angle of circle O and that angle ACB is a circumscribed angle of circle O. We see that AO ≅ BO because .
We also know that AC ≅ BC since .
Using the reflexive property, we see that .
Therefore, we conclude that △ACO is congruent to △BCO by the .