Question

A chord in circle T has a length of 16 cm and the diameter of the circle 20 cm. How far is the chord from the center of the circle

Answer 1

ANSWER

$6\operatorname{cm}$

EXPLANATION

First, let us make a sketch of the circle:

Since the diameter of the circle is 20 cm, the radius of the circle is 10 cm, as shown above.

The two radii and the chord of the circle form a triangle. Also, the distance from the center to the chord forms a right triangle with the radius and half the length of the chord:

Now, we can solve for d by applying the Pythagoras theorem:

$10^2=d^2+8^2$

Solve for d:

$\begin{gathered} d^2=10^2-8^2 \\ d^2=100-64=36 \\ d=\sqrt[]{36} \\ d=6\operatorname{cm} \end{gathered}$

That is the distance from the chord to the center of the circle.