The chord AB is equal to 18cm OA and OB are the radii of the circle and the angle AOB = 90 degrees.

The chord AB is equal to 18cm OA and OB are the radii of the circle and the angle AOB = 90 degrees. Find the distance from point O to chord AB.

The chord AB and the radii of the circle OA and OB form a triangle AOB. Triangle AOB is rectangular (since the angle AOB = 90 degrees) isosceles (since OA = OB). The distance from point O to chord AB is the height of the triangle AOB – OH. In an isosceles triangle, the height and median, drawn to the base of the triangle, are equal to each other. In triangle AOB, the base is the hypotenuse AB, then OH is both the height and the median. In a right-angled triangle, the median drawn to the hypotenuse is equal to half the hypotenuse, that is:
OH = AB / 2 = 18/2 = 9 (cm).
Answer: OH = 9 cm.