Question

The length of a chord of a circle of 16.8cm, radius is 9.1cm. Find its distance from the centre. ​

Answer 1

Distance from the center is 3.5 cm.

Step-by-step explanation:

Given : The length of a chord of a circle of 16.8 cm radius is 9.1 cm.

To find : Its distance from the center ?

Solution :

Refer the attached figure below.

By theorem,

Radius from the center perpendicularly bisect the chord of the circle.

⇒ $AC=\frac{1}{2}AB=\frac{1}{2}\times 16.8=8.4\ cm$

In ΔOCA,

By Pythagoras theorem,

$OA^2=AC^2+OC^2$

$(9.1)^2=(8.4)^2+d^2$

$82.81-70.56=d^2$

$d^2=12.25$

$d=3.5$

 Therefore, distance from the center is 3.5 cm.