Think Logically not mathematically [part-30]

Geometry Level 1

If the circumcircle and the incircle of a triangle are concentric circles, then what type of triangle is it?

Isoceles right angled triangle Cannot be determined Right angled triangle Equilateral triangle

Sudoku Subbu by sudoku subbu , 19, India

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2 solutions

Rindell Mabunga
Jun 25, 2016

Equality case for Euler's Theorem in Geometry

2 Helpful 0 Interesting 0 Brilliant 0 Confused

Can you explain in more detail? Why does the concentric circles imply that we must be in the equality case?

Calvin Lin Staff - 4 years, 11 months ago
Sudoku Subbu
Jun 25, 2016

In a Equilateral Triangle the Circumcentre and the Incentre coincides. Therefore the circles formed by the same origin will be Concentric circles. Therefore the type of Triangle is Equilateral.

1 Helpful 0 Interesting 0 Brilliant 0 Confused

All that you have shown is that equilateral triangles satisfy the conditions. You have not shown that only equilateral triangles satisfy the conditions. It is still possible for the answer to be (say) isosceles triangles, or "some set with no clear description".

Calvin Lin Staff - 4 years, 11 months ago

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