Find the radius of the circle if the chord 24cm long is 5cm from the center of the circle.

The triangle ΔAOB is isosceles, since its lateral sides are the radii of the given circle:

AO = OB.

The segment OH is the height of this triangle, and is also the distance from the center of the circle to the chord AB.

Since the height of an isosceles triangle divides it into two, equal to each other, right-angled triangles. Consider one of them, ΔAOH.

To calculate AO, we apply the Pythagorean theorem:

AO ^ 2 = OH ^ 2 + AH ^ 2;

AH = AB / 2;

AH = 24/2 = 12 cm.

AO ^ 2 = 5 ^ 2 + 12 ^ 2 = 25 + 144 = 169;

AO = √169 = 13 cm.

The segment AO is the radius of the circle.

Answer: the radius of the circle is 13 cm.