   SEARCH HOME Math Central Quandaries & Queries  Question from Maty, a student: How do i find the area of a triangle inscribed a circle while another smaller circle is circumscribed by the same triangle and the radius is 8. Maty,

You need more information. In general you need three pieces of information to fix a triangle. Even if you are given the radii of both the inner and the outer circles, there would be infinitely many different sized triangles inscribed in the larger circle and circumscribed about the smaller.

We have attached an interactive picture. You can adjust the radius of either circle and drag the vertex A about the larger circle. Note that as A moves, the area of triangle ABC changes even though the incircle and circumcircle stay fixed. The largest and smallest are the isosceles triangles with one vertex on the line OI.

Please enable Java for an interactive construction (with Cinderella).

Created with Cinderella

Chris     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.