Side AB of triangle ABC passes through the center of a circle of radius 25 circumscribed about it. Find AC if BC = 48.

1. Since the side AB of the triangle ABC coincides with the diameter of the circle, then:

AB = 2r = 2 * 25 = 50.

2. ABC is a triangle inscribed in a circle, one side of which is the diameter of this circle, hence ABC is a right-angled triangle with hypotenuse AB. Along the tower of Pythagoras:

BC ^ 2 + AC ^ 2 = AB ^ 2;

AC = √ (AB ^ 2 – BC ^ 2) = √ (50 ^ 2 – 48 ^ 2) = √ (2500 – 2304) = √196 = 14.

Answer: AC is 14.