# finding the radius of the circle given a coordinate

find the radius of the circle with center at (-1,2) if a chord of length 10 is bisected at (4,-3).(this is exactly what our professor given to us)

im thinking of using the distance formula which is

d=√(x2-x1)^2+(y2-y1)^2

but our topic is about division of line segment but i think i cant use that because the problem is about finding the length of radius of a circle link of the formula

and ive tried to graph it, but i dont know if it is correct.

my graph

this is according on my understanding

• Commented Jan 15, 2016 at 17:51
• @labbhattacharjee sorry i didn't understand the link :( Commented Jan 15, 2016 at 17:56
• I am surprised that the problem has a unique solution. Bisection of a chord seems to be a rather strong property of a given line through a circle. Commented Jan 15, 2016 at 18:03

As the perpendicular bisector of any chord of any given circle must pass through the center O$(-1,2)$ of that circle.
If $P(4,-3)$ is midpoint of the chord and $R$ is one of the extreme points,
$OR^2=OP^2+PR^2, PR=5$ unit