Question

A chord of 12 cm long is drawn into a circle of diameter 20cm.The distance of chord from center.

Answer 1

Given $A$ circle with center $O$ Radius $OA=10$ cm chord $AB=12$ cm.

To find the distance $OM$ of the chord from $O$

$OM$ is perpendicular to chord $AB$

As perpendicular from the center $Na$ chord bisect the chord. So $AM=\frac{AB}{2}=6$ cm

In right angled triangle $AMO$

${AO}^2={AM}^2+{OM}^2$

$\Rightarrow {10}^2=6^2+{OM}^2$

$\Rightarrow 100=36+{OM}^2$

$\Rightarrow {OM}^2=100-36$

$\Rightarrow {OM}^2=64$

$OM=8cm$