Formulate and prove the tangent property theorem.

Theorem.
A tangent drawn to a circle creates a right angle with a radius drawn to the tangent point.
Evidence.
Let us be given a circle centered at point O. Let the tangent t to this circle touch the circle at point R. So we will consider the radius OR.
We need to prove that the line t is perpendicular to the radius of the circle OR.
We will prove it by contradiction.
Suppose t is not perpendicular to OR.
In this case, the radius of the circle OR will be inclined to the straight line t. The perpendicular, which in this case can be drawn from the center of the circle O to the straight line t, must be shorter than the oblique OR. We conclude that the distance from the center of the circle of point O to the straight line t is less than the radius. This means that the line t and the circle will have two common points, that is, the line t is a secant. The obtained assertion contradicts the hypothesis of the theorem, since t is defined as a tangent to the circle.
Making an assumption, we got a contradiction. Therefore, we conclude that the assumption is not true and the line t is perpendicular to the radius OR.
Thus, a tangent drawn to a circle creates a right angle with a radius, which is drawn to the tangency point.
The theorem is proved.