Circle Inscribing

If r is the inradius of a circle inscribed in a right triangle with sides a and b and hypotenuse c, then

A Sangaku problem dated 1803 from the Gumma Prefecture asks to construct the figure consisting of a circle centered at O, a second smaller circle centered at O_2 tangent to the first, and an isosceles triangle whose base AB completes the diameter of the larger circle through the smaller XB. Now inscribe a third circle with center O_3 inside the large circle, outside the small one, and on the side of a leg of the triangle. It then follows that the line O_3A_|_XB. To find the explicit position and size of the circle, let the circle O have radius 1/2 and be centered at (0,0) and let the circle O_2 have diameter 0<r<1. Then solving the simultaneous equations

for a and y gives

See also

Explore with Wolfram|Alpha

References

Referenced on Wolfram|Alpha

Cite this as:

Weisstein, Eric W. "Circle Inscribing." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/CircleInscribing.html

Subject classifications