A tangent AB, A-tangency point is drawn to the circle with center O. Find the radius of the circle if AB = 2√5, OB = 6.

Since the tangent is perpendicular to the radius of the circle drawn to the point of tangency, in our case the radius of the AO is perpendicular to the tangent AB.

Therefore, triangle OAB is right-angled with right angle A.

And, therefore, the radius of AO can be found by the Pythagorean theorem:

(AO) ^ 2 = (OB) ^ 2 – (AB) ^ 2 = 6 ^ 2 – (2√5) ^ 2 = 36 – 20 = 16.

AO = 4.

Answer: the radius of the circle is 4.