Question

A circle is radius 5cm find the length of the chord of distance 3cm from its centre

Answer 1

Answer:

The length of the chord of distance 3cm from its centre is 8cm.

Step-by-step explanation:

Given radius of the circle (AC) = 5 cm  

AO =3 cm

Consider the triangle AOC, which is a right angled triangle.

By applying Pythagoras theorem, we can write,

$\begin{array}{l}{\mathrm{AO}^{2}+\mathrm{OC}^{2}=\mathrm{AC}^{2}} \\ {3^{2}+\mathrm{OC}^{2}=5^{2}} \\ {9+\mathrm{OC}^{2}=25} \\ {\mathrm{OC}^{2}=16}\end{array}$

Taking square root,  

OC = 4,

Therefore the length of the chord = 4 + 4 = 8 cm.

Answer 2

Answer:

8cm

Given:-

Length of radius = 5cm

Distance of, From center = 3cm

TO FIND :-

Length of chord

Step By Step Explaination :-

Let the length of Length of chord be 'C' cm.

Also,

The shortest distance between any points is the perpendicular between them.

So, since its a perpendicular, distance,

Using PYTHAGORAS THEOREM.

=> 5²= C²+3²

=>25=C²+9

=> 25-9=C²

=> 16=C²

=> √16=C

=> C=±4cm

also,on the other side it will also be 4 cm,since we talk only of one side.

So, 4+4cm =8cm

Since, Its length cannot be negative, so taking it as positive.

So, the value or length of chord subtended in the circle is 8cm.

Ans.