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

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.

Since AB touches the circle, the radius OB drawn to the segment AB will be perpendicular to AB. Then the ABO triangle is a right-angled triangle, in which AB = 48 is the leg, OB = 14 is the second leg, and AO is the hypotenuse. Let us find the hypotenuse of AO by the Pythagorean theorem:
AO ^ 2 = AB ^ 2 + OB ^ 2;
AO = √ (AB ^ 2 + OB ^ 2);
AO = √ (48 ^ 2 + 14 ^ 2) = √ (2304 + 196) = √2500 = 50 (conventional units).
AO hypotenuse consists of two segments AD and DO. The DO segment is the radius, so DO = 14. Then:
AO = AD + DO;
50 = AD + 14;
AD = 50-14;
AD = 36 conventional units.
Answer: AD = 36 conventional units.