Question

The radius of a circle is 5cm .The distance of a chord from the center is 4 cm. Find the length

of the chord .​

Answer 1

Answer:

6CM

LET

AB = 5CM

AD= 4CM

BY USING PYTHAGORAS THEOREM

AB^2 = AD^2+ BD^2

5^2= 4^2 + BD ^2

BD ^2= 25-16

BD^2 = 9

BD = √9

BD = 3cm

BC = 2BD

2×3= 6cm

I hope it will help you

Answer 2

Concept:-

Here, We have given the radius of the circle and the distance of the chord from the centre. We have to find the length of the chord.  We will use here the theorem " Perpendicular drawn from the centre of the circle bisects the chord ".

Given:-

• Radius of the circle is 5 cm.
• Distance of a chord from the centre is 4 cm.

To Find:-

• Length of the chord ?

Solution:-

Here, Distance of the chord from the centre of the circle (OR) = 4 cm.

And, Radius of the circle is (PO) = 5 cm

By Pythagoras theorem We have,

$\sf{\Longrightarrow (PR)^{2} = (PO)^{2} - (OR)^{2}}$

$\sf{\Longrightarrow (PR)^{2} = (5)^{2} - (4)^{2}}$

$\sf{\Longrightarrow (PR)^{2} = 25 - 16}$

$\sf{\Longrightarrow (PR)^{2} = 9}$

$\sf{\Longrightarrow PR = \sqrt{9}}$

$\sf{\Longrightarrow PR = 3\ cm}$

Since, The perpendicular drawn from the centre of the circle to the chord bisects the chord.

∴  PR + RQ = 3 + 3 = 6 cm

Hence, Length of the chord is of 6 cm.