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Triangle heights

Question

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Call the altitudes of a triangle: h , k , m; and the radius of its inscribed circle: r.
Find the minimum value of the expression (h + k + m) / r (over all triangles).
Which triangle achieves this minimum?

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2 answers to this question

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the biggest (h+k+m)/r is when r approach zero. the biggest r that fits in a triangle is in an equilateral one.

How do you know this?

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