Question

A chord of length 24 cm is drawn at a distance of 5 cm from the centre of a circle.Find the radius of the circle.


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Answer 1

Answer:

Step-by-step explanation:

Chord of a circle = 24 cm.

Distance of chord from centre of the circle = 5 cm

Radius of the circle = [(24/2)^2+5^2]^0.5 = [144+25]^0.5 = 13 cm.

Area of the circle = (22/7)*13^2 = 531.14 sq cm.

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Answer 2

Given:

A chord of length 24 cm is drawn at a distance of 5 cm from the centre of a circle

To Find:

Find the radius of the circle.

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 5cm which means that the perpendicular drawn from the centre to the chord has a length of 5 cm. And the length of the chord is 24cm.

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.

So now in triangle OPB, we will use Pythagoras theorem,

where,

OP=5cm

PB=12cm

OB= r

$OB^2=OP^2+PB^2\\r^2=5^2+12^2\\r=\sqrt{25+144} \\r=13cm$

Hence, the radius of the circle is 13 cm.