The distance from the point of the circle to the ends of the diameter is 9cm and 12cm. Find the radius of the circle.

From the condition it is known that the distance from the point of the circle to the ends of the diameter is 9 cm and 12 cm. And we need to find the radius of the circle.

As a result, we will consider a triangle, which is formed by the diameter of the circle and chords drawn to the ends of the diameter from different points.

The resulting triangle will always be rectangular, the diameter of the circle will be its hypotenuse.

We apply the Pythagorean theorem to the triangle and get the length of the diameter:

c ^ 2 = a ^ 2 + b ^ 2;

c = √ (a ^ 2 + b ^ 2) = √ (9 ^ 2 + 12 ^ 2) = √ (81 + 144) = √225 = 15 cm.

R = d / 2 = 15/2 = 7.5 cm.