Question

the radius of a circle is 10 centimetres and the length of one of its chords is 12 centimetres find the distance of the chord from the centre

Answer 1

let AB be the chord.
OA is the radius.
OC bisects the chord as it is from centre and  forms  right angle .
in triangle OCA ,
AC =6 cm(as radius bisects)
OA=10cm (radius)

we must find OC (distance from centre)

using pythagoras theorem,
OC^2 + AC^2 = OA ^2
OC^2 = 100 - 36
OC^2 = 64
OC = 8cm
thus distance of chord is  8 cm.

hope it helps!!!!

Answer 2

Hi there !!

AB is the chord here

OA is the radius
=========================================

OA = 10 cm

AB = 12 cm

We know that ,

a line segment drawn from the centre of a circle to the chord , bisects the chord.

This means that the line segment OC which is drawn from the centre bisects the chord AB.

Also ,
OC is perpendicular to AB

hence,

AC = 1/2 AB
= 6 cm

Consider Δ AOC.


Δ AOC is a right angled triangle.

So ,
according to Pythagoras theorem :

OA ² = AC² + OC²

10² = 6² + OC²

OC² = 10²- 6²

= 100 - 36

= 64

OC = √64

= 8cm

hence ,
distance of the chord from the centre = 8cm