Out of sight...
Geometry
Level
2
Given the three excircles of a triangle. Can the triangle be uniquely defined?
Cannot be determined.
No.
Yes.
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1 solution
Given two excircles, draw a pair of crossed tangents to both circles, and then draw another that is tangent to both. Then there is only one variable, which is the angle the cross tangents make with each other. This angle can vary from 0 to 180, as the distance between the first two excircles vary from 0 to infinity. There will exist one and only one angle will it be possible for the 3rd excircle to be tangent to all three.