ABC and XYZ are similar triangles and the circumcircle of the triangle XYZ is the incircle of the triangle ABC. If k = Area of ABC/Area of XYZ, then find the minimum value of k.

The minimum value of k would be where ABC and XYZ are equilateral triangles.
The length of each side of XYZ would be equal to half the length of each side of ABC.
If we let length of one side of XYZ equal to one unit,
the area of triangle XYZ is equal to SQRT(3)/4 units, and
the area of triangle ABC would be equal to SQRT(3) units.
Given k = Area of ABC/Area of XYZ, i.e., SQRT(3)/SQRT(3)/4, k would equal 4.

Edited on May 26, 2009, 2:27 pm

Posted by Dej Mar on 2009-05-26 14:26:45