Question

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

Answer 1

The distance of the chord from the centre of the circle is 6 cm.

Answer 2

The distance of the chord from the center of the circle is 6 cm.

Let the blue line represent the circle chord whereas, red line is the circle radius.

The yellow line is the line from the circle to chord of the circle which is perpendicular.

Given that the chord length = 16 cm,

the perpendicular intersection point from centre to chord which breaks the length equally into two phrases, so that its radius is 10cm and right half-length is 8cm.

By Applying Phythagoras theorem, we get

The distance from the center to the chord  

$\begin{array}{c}{=\sqrt{\left(10^{2}-8^{2}\right)}} \\ {=\sqrt{100-64}} \\ {=\sqrt{36}} \\ \bold{=6}\end{array}$.