Question

A chord of a circle is of length 6 CM and it is at distance of 4 CM from centre. Find the radi of the circle.

Answer 1

Answer:

Step-by-step explanation:

the chord of a circle (PQ)=?

distance of the chord from the centre(OR)=4cm

radius of the circle(OP)=5cm

By Pythagoras theorem,

OPsq.=OR sq.+PR sq.

5sq.=4 sq.+PR sq.

25 =16 +PR. sq.

PR sq.=25-16

PR sq. =9cm

therefore PR=3cm

PR +QR=3+3= 6cm(the perpendicular drawn from centre to chord bisects the chord.

therefore length of the chord is 6 cm

Answer 2

Given:

A chord of a circle is of length 6 CM and it is a distance of 4 CM from the centre.

To Find:

Find the radius of the circle.

Solution:

We are given that a chord is at a distance of 4cm from the centre of the circle hence, we need to find the radius of the circle,

The chord is a distance between any two points on the circumference also the longest chord is known as the diameter.

The perpendicular drawn from the centre to the chord of the circle bisects the chord into 2 equal parts.

So the chord perpendicular distance and radius forms a right-angled triangle with the radius as the hypotenuse,

Applying the Pythagoras theorem which states that the square of the hypotenuse is equal to the sum of the squares of base and the perpendicular, we have,

$r^2=3^2+4^2\\r^2=9+16\\r=\sqrt{25} \\r=5cm$

Hence, the radius of the circle is 5cm.