please help!

Question

Supose the diameter of a circle is 50 feet long and has a chord of 48 feet long. What is the distance from the center of the circle to the chord.

Answer 1

As the diagram below,

chord (AB) = 48 feet.

Diameter (CD) = 50 feet.

Center of the circle is O,radius (OA) = CD/2 = 50/2 = 25 ft.

M is the midpoint of AB. So, AM = AB/2 = 48/2 = 24.

Since, OM is perpendecular to AB,we have AO^2 = AM^2 + OM^2.

SO, OM^2 = AO^2 - AM^2

                = 25^2 - 24^2

                = 625 - 576

                = 49.

OM = sqrt (49) = 7 ft.

Hence, the distance from the center of the circle to the chord is 7 ft.