Question

In a circle of diameter 30 cm a chord of 10cm is drawn. To 2 decimal places, how far is the chord from the center of the circle?

Answer 1

Given:

The circle has a diameter of 30 cm and a chord of 10 cm is drawn.

Radius of the circle = 15 cm

Half of the chord = 5 cm

We need to determine the distance of chord from the center of the circle.

Distance of chord from the center of the circle:

Let us use the Pythagorean theorem, to find the distance between the center and the chord.

Let d denote the distance between the center and the chord of the circle.

Thus, we get;

$15^2=d^2+5^2$

$225=d^2+25$

$200=d^2$

Taking square root on both sides, we get;

$14.14=d$

Thus, the distance between the center and the chord of the circle is 14.14 cm.

Hence, Option A is the correct answer.