Math CentralQuandaries & Queries


Daryl, a student:

Find the equation of the smaller circle that is tangent to the axes and the circle x2+y2=2x+2y-1?

Hi Daryl,

If you put the circle equation in standard form you will see that is the circle with centre (1, 1) and radius 1. That's the black circle in my diagram.
Hence |OP| = |PC| = 1 and using Pythagoras theorem |CO| = sqrt(2).
Let r be the radius of the small circle.
Triangle COP and AOB are similar and hence 1/sqrt(2) = |BA|/|AO|
But |BA| = r and |AO| = |CO| - (|CT| + |TA|). Substitute into the equation on the previous line and solve for r.


About Math Central


Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.
Quandaries & Queries page Home page University of Regina PIMS