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

Question

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

Accepted Answer

Consider AB as the chord with O as the centre and radius 10cm

R S Aggarwal Solutions - Mathematics - Class 9 chapter Circles Question 1 Solution image

So we get

OA = 10 cm and AB = 16cm

Construct OL ⊥ AB

The perpendicular from the centre of a circle to a chord bisects the chord

So we get

AL = ½ × AB

By substituting the values

AL = ½ × 16

So we get

AL = 8 cm

Consider △ OLA

Using the Pythagoras theorem it can be written as

OA^2 = OL^2 + AL^2

By substituting the values we get

10^2 = OL^2 + 8^2

On further calculation

OL^2 = 10^2 - 8^2

So we get

OL^2 = 100 – 64

By subtraction

OL^2 = 36

By taking the square root

OL = √36

So we get

OL = 6cm

Therefore, the distance of the chord from the centre of the circle is 6cm.

RS Aggarwal Solutions Class 9 Mathematics Solutions for Circles Exercise 12A in Chapter 12 - Circles