The chord of the circle, perpendicular to the diameter, divides its parts equal to 24 cm and 6 cm. Find the length of this chord.

We draw from point O the segments OC and OD, then the triangle OCD is isosceles OC = OD = R.

Since CD is perpendicular to AB, the segment OH is the height, bisector and median of the triangle COD. Then CH = DH = CD / 2.

By the property of intersecting chords, the product of the lengths of the segments formed by the intersection point of one chord is equal to the product of the lengths of the segments of the other chord.

AH * BH = CH * DH = CH ^ 2.

6 * 24 = CH ^ 2.

CH ^ 2 = 144.

CH = 12 cm, then CD = 2 * CH = 2 * 12 = 24cm.

Answer: The chord length is 24 cm.