Question

Find the radius of a circle using the Pythagorean theorem, given that the center is at (1, 5) and the point (5, 1) lies on the circle. 32−−√ units 12−−√ units 72−−√ units 50−−√ units

Answer 1

Given :

Center of circle, C = ( 1 , 5 )

Point on circle, P = ( 5 , 1 )

To Find :

The radius of a circle.

Solution :

We know, radius of circle is the distance between center and point of circle.

Distance between two points A(p,q) and B(r,s) is given by :

$D = \sqrt{(p-r)^2+(q-s)^2}$

So, distance between the points (1, 5) and (5, 1) is :

$D = \sqrt{(1-5)^2+(5-1)^2}\\\\D = 5.66 \ units$

Therefore, radius of circle is 5.66 units.

Hence, this is the required solution.