Line segment AB = 48 touches circle of radius 14 with center O at point B. The circle intersects segment AO

Line segment AB = 48 touches circle of radius 14 with center O at point B. The circle intersects segment AO at point D. Find AD.

If the line segment touches the circle, then the radius drawn to the tangency point is perpendicular to the line segment. This means that the angle formed by the radius OB and the segment AB is a straight line. Triangle AOB – rectangular. Let’s find AO according to the Pythagorean theorem: The square of the hypotenuse is equal to the sum of the squares of the legs. We have AO – hypotenuse, OB and AB – legs.

AO ^ 2 = AB ^ 2 + OB ^ 2;

AO ^ 2 = 48 ^ 2 + 14 ^ 2 = 2304 + 196 = 2500;

AO = 50.

OD is the radius of the circle, OD = 14.

AD = AO – OD;

AD = 50 – 14 = 36.

Answer. 36.