Distance from the center of the circle O to the chord CD = 13cm. Corner COD = 90 degrees. Find the chord length CD.

The distance from the center of the circle to the chord СD is the perpendicular OH drawn from point O to the chord СD.
Then the angle OНС = OНD = 900, and the triangles OCH and ODН are rectangular.
Let us construct the radii of the OС and OD, then the triangle of the OСD is isosceles, and then the height of the OH is also its median, and the bisector, which means CH = DН = СD / 2, the angle СOН = 90/2 = 450.
Then the triangle СOН is rectangular and isosceles, CH = OH = 13 cm.
СD = 2 * CH = 2 * 13 = 26 cm.
Answer: the length of the СD chord is 26 cm.