A geometry problem by A Former Brilliant Member

The tangents to a circle drawn from an external point are equal, and make equal angles with the line joining the point to the center. A tangent line makes an angle of 90 degrees with the radius of the circle.

inscribed angle = $\frac{1}{2}$ $intercepted$ $arc$

$<ADC$ $=$ $\frac{1}{2}$ $(65$ )( $2$ ) $=$ $\boxed{65^\circ}$