The perpendicular dropped from the point of the circle by the diameter divides it into segments in the ratio of 9:16.

The perpendicular dropped from the point of the circle by the diameter divides it into segments in the ratio of 9:16. The radius of the circle is 25 cm. Find the length of the perpendicular.

СН – perpendicular lowered to the diameter AB from the point of the circle C.

AH: HB = 9: 16; AH is 9/25 of the diameter;

AB = 2 R = 2 * 25 = 50 (cm);

AH = 50: 25 * 9 = 18 (cm);

HO = AO – AH = 25 – 18 = 7 (cm);

The OS triangle is rectangular.

CH² = OC² – HO² = 25² – 7² = 625 – 49 = 576 (cm²);

CH = √576 = 24 (cm).