Through point A, not lying on the circle, draw tangents AB and AC to this circle.

Through point A, not lying on the circle, draw tangents AB and AC to this circle. Points B and C are tangency points. Prove that AB = AC.

Let’s build the radii of the OB and OС to the points of tangency. The radii OB and OS are perpendicular to the tangent AB and AC, then the triangles AOB and AOC are rectangular.

In right-angled triangles AOB and AOC, the hypotenuse of AO is common, leg OB = OС = Р, then triangles AOB and AOC are equal in leg and hypotenuse, and then AB = AC, which was required to be proved.