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Challenge 104: Isoceles Circles

Can you find the radius of this circle in a isosceles triangle?

An isoceles triangle has side lengths 7, 7 and 2. Find the radius of the circle that goes through each of its vertices.

Generalise to an isoceles triangle of side lengths a, a and b.

Can you generalise any further, to consider a general triangle with side length a,b and c? Is your result consistent with your previous answers?