Given that is a tangent to the circle , and , determine .
A tangent to a circle is perpendicular to the radius at its point of tangency.
is a tangent to the circle so, , and triangle
The sum of the interior angles of a triangle is , so for
, , and are collinear so is the exterior angle of
triangle . We can use the Triangle Exterior Angle Theorem which
We can see that (radii), so triangle is isosceles, and .
From the Exterior Angle Theorem, we had
But , so