Question

Suppose the diameter of a circle is 26 cm long, and a chord is 24 cm long. Find the distance from the center of the circle to the chord.

a) 5 cm
b) 10 cm
c) 12 cm
d) 13 cm

Answer 1

The distance from the center of the circle to the chord is 5 cm.

Step-by-step explanation:

To find the distance from the center of the circle to the chord, we can use the Pythagorean theorem. The chord, which is 24 cm long, is divided into two equal parts by the center of the circle. Each part is half the length of the chord, so it is 12 cm. Now, we can use the Pythagorean theorem to find the distance from the center to the chord. Let's call this distance 'd.' Using the theorem, we have:

d^2 = (26/2)^2 - 12^2

d^2 = 169 - 144

d^2 = 25

d = 5

Therefore, the distance from the center of the circle to the chord is 5 cm.