Q on circles: 1st has r=5, (h,k) = (0,5), 2nd has r=12, (h,

[monkeyjo]

This problem has to do with finding the center of a circle given the centers of two other circles.

One circle has a radius of 5 and its center is (0,5). A second circle has a radius of 12 and its center at (12,0). What is the length of a radius of a third circle which passes through the center of the second circle and both points of intersection of the first 2 circles?

 

[Deleted member 4993]

Re: Question about circles

This problem has to do with finding the center of a circle given the centers of two other circles.

One circle has a radius of 5 and its center is (0,5). A second circle has a radius of 12 and its center at (12,0). What is the length of a radius of a third circle which passes through the center of the second circle and both points of intersection of the first 2 circles?

Please show your work - indicating exactly where you are stuck.

To start off - find the points of intersections of the given two circles.

 

[pka]

Any three non-collinear points determine a circle.
Consider two line segments determined by those points.
Construct the perpendicular bisectors of those.
The point of their intersection is the center of the sought after circle.

 

[Deleted member 4993]

Are you supposed to solve this problem by geometric construction (compass & straight-edge) or by analytical method?

In either case - sketch the approximate situation - you'll get clues to short-cuts.