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.

One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.