Question

A circle of centre M (3, 2) is given. Any point N (5, 6) is on the circumference of the circle. Then find the length of the radius MN.​

Answer 1

Answer:

 √ 20= 2 √ 5

Step-by-step explanation:

The centre of the given circle is at (3,2)

Point of circle is(5,6)

the distance between two points is

= √ (3-2)² +(2-6)²

= √ (4+16)

=2 √ 5

Answer 2

Given,

A circle of center $M(3,2)$ is given. Any point $N(5,6)$ is on the circumference of the circle.

Formula,

Distance $=\sqrt{(x_{2}-x_{1} )^{2}+(y_{2}-y_{1} )^{2} }$

Here, $x_{1}=3, x_{2}=5$

$y_{1}=2, y_{2}=6$

Substitute the given values in the formula,

$d=\sqrt{(5-3)^{2}+(6-2)^{2} }$

$d=\sqrt{2^{2}+4^{2} }$

$d=\sqrt{4+16}$

$d=\sqrt{20}$

$d=\sqrt{4\times5}$

$d=2\sqrt{5}$

Therefore, the length of the radius $MN$ is $2\sqrt{5}$.