Question

A chord of length $12$ cm is drawn in a circle of radius $10$ cm. Calculate its distance from the centre of circle.

Answer 1

Let $AB=12$ cm be the chord of the circle with radius $AO=10$ cm

Draw $OP\perp AB$ Join OA

$AP=\frac{1}{2}AB=\frac{1}{2}\times 12=6cm$

In $△APO,\angle P={90}^{\circ }$

$\therefore A{O}^2=A{P}^2+O{P}^2$

$\Rightarrow {10}^2=6^2+O{P}^2$

$\Rightarrow O{P}^2=100-36$

$\Rightarrow O{P}^2=64$

$\Rightarrow OP=8cm$

Hence the distance of the chord from the circle is $8$ cm.