The perpendicular drawn from the point of the circle to the diameter divides it in the ratio of 9:16.

The perpendicular drawn from the point of the circle to the diameter divides it in the ratio of 9:16. Find the diameter of the circle if the perpendicular is 36 cm.

Let the length of the segment AH = 9 * X cm, then CH = 16 * X cm.

Let’s build chords AB and BC.

The inscribed angle ABC is based on the diameter of the AC, then the triangle ABC is rectangular, and the perpendicular BH is the height from the right angle to the hypotenuse.

Then BH ^ 2 = AH * CH.

BH ^ 2 = 9 * 16 * X ^ 2.

BH = 3 * 4 * X = 36.

X = 3.

Then AH = 3 * 9 = 27 cm, CH = 3 * 16 = 48 cm.

AC = 27 + 48 = 75 cm.

Answer: The diameter of the circle is 75 cm.