How many Heronian II
Geometry
Level
5
How many other non-congruent Heronian triangles have same Steiner inellipse as triangle with sides 20, 21, 29?
None of the answers here
0
2
8
Infinitely many
16
1
4
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1 solution
In order for two triangles to share the same Steiner inellipse they need to have the same areas, so we need to look at Heronian triangles with area 2 1 0 . Here is a list of triangles that qualify:
a-b-c: 68-65-7, 37-35-12, 39-28-17, 28-25-17, 29-21-20
Applying formulas found here we can not match any other triangle to produce the same values for semi-axes. Therefore the answer is 0 .