Question

A chord of length 16 cm is drawn in a circle of radius 10 cm. Find the distance of the chord from the centre of the circle.

Answer 1

From the figure shown,

Radius$=OA=10cm.$

$AB$ is the chord drawn with the length$=16cm$.

We know,

perpendicular drawn from the centre of the circle to the chord ,bisects the chord

hence, $C$ is the midpoint of $AB$.

Therefore,

$AC=\frac{AB}{2}=\frac{16}{2}=8$

So using Pythagorean Theorem:

$O{A}^2=O{C}^2+A{C}^2$

${10}^2=O{C}^2+8^2$

$100=O{C}^2+64$

$O{C}^2=36$

$OC=6cm$