We can fill all the blanks with help of below explanation.
Explanation:
Given: is a central angle and is a circumscribed angle. (where, AC and CB are two tangent lines from an external point C.)
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 because both OA and OB make the radius of the circle O. (Since, A and B are points on the circumference of circle O So, they are equally far from the center O
We also know that since both are the tangent line from a common point C So, they must be equal.(By the property of tangent line)
Using the reflexive property, we see that
Therefore, we conclude that by the SSS postulate.