In a circle centered at point O and radius OC = 25, a chord CD = 40 is drawn. Find the distance from the center

In a circle centered at point O and radius OC = 25, a chord CD = 40 is drawn. Find the distance from the center O to the chord CD.

In the triangle OCD we draw the height OH, which will be the distance from the center O to the chord CD.
Triangles OCH AND ODH are equal, since the height OH in an isosceles triangle OCD divides this triangle into two equal ones.

The OCH triangle is rectangular. Leg CH = HD = (40/2) = 20, since OH is both the height and the median in the isosceles triangle OCD.
We find the OH leg in a right-angled triangle OCH by the Pythagorean theorem.
OH = √ [(OC) ^ 2 – (HC) ^ 2] = √ [(25) ^ 2 – (20) ^ 2] = √ (625 – 400) = √ (225) = 15.