Question

a chord of length 12 cm of a circle is at a distance of 8cm from its centre. find the radius.

need step by step explaination...​

Answer 1

GIVEN : Length of chord = 12 cm , Distance of chord from centre = 8 cm.

TO FIND: Radius of circle.

SOLUTION:

A perpendicular from centre to a chord bisects the chord,

So , half chord = 6 cm

Using Pythagoras theorem,

r = root ( 36 + 64)

r = root (100)

r = 10 cm

HENCE, Radius of circle is 10 cm.

Answer 2

Given:

a chord of length 12 cm of a circle is at a distance of 8cm from its centre.

To Find:

Find the radius

Solution:

A chord is a line segment from one point of the circle to the other. It is given that the distance of the chord from the centre of a circle is 8cm which means that the perpendicular drawn from the centre to the chord has a length of 8 cm.

So we can see a triangle forming by joining the two ends of the chord with the centre and each triangle formed is a right-angled triangle

Now to find the length of the radius we will use the Pythagoras theorem in one of the triangles formed,

In triangle OPB,

OP=8cm

PB=6cm

OB=r

Now,

[tex]OP^2+PB^2=OB^2\\ 8^2+6^2=r^2\\ r=\sqrt{64+36} \\ r=10cm[/tex]

Hence, the length of the radius is 10cm.