Question

How to use the distance formula to find the radius of a circle?

Answer 1

Hint: The distance formulae for which the above question is asking for is the formula which gives the length of the line segment drawn between two points, to obtain the length we have to use it, the formulae can be used between two points say (a,b) and (c,d) as:
\[ \sqrt {{{(a - c)}^2} + {{(b - d)}^2}} \]

Formulae Used:
\[ \sqrt {{{(a - c)}^2} + {{(b - d)}^2}} \]length of line segment drawn between two points say (a,b) and (c,d).

Complete step-by-step answer:
Here the given question need to find the length of the radius of any circle for which we have to use the distance formulae for length between two points,
Here the question has not given the coordinates of the centre as well as the equation of circle is also not given, so assuming an circle with centre at (0,0) and say it cut the x- axis at any point say (b,0), hence the coordinate are now assumed, now applying distance formulae to get the length of the radius of the circle we get:

\[ \Rightarrow radius = \sqrt {{{(0 - b)}^2} + {{(0 - 0)}^2}} = \sqrt {{b^2}} = b\]
Here for any coordinate given we will formulae in the same manner and get the result.

Note: Here in the above question, to find the radius of the circle we can also use the graph plotting, in which we can simply plot the circle on the graph and then we can count the distance from centre to the curve of circle and will obtain the radius of the circle as per requirement according to question.