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If the altitudes p₁, p₂, and p₃ of a triangle enclose a circle with a diameter of 4/3 units, what is the minimum possible value of p₁ + p₂ + p₃?

1. 4
2. 5
3. 6
4. 7

Correct answer: 6

Solution

The altitudes enclose a circle with a fixed diameter, and their sum is minimized when the triangle is equilateral. For this configuration, the minimum value of p₁ + p₂ + p₃ is 6.

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