Theorem 2. Let ABC be any triangle, with a = |BC|, b = |CA|, c = |AB|, and area ∆. If XY Z is inscribed in ABC, then
|XY | + |Y Z| + |ZX| ≥ 8∆
2
abc . (1)
Equality holds in (1) if and only if ABC is acute-angled; and then only if XY Z is its orthic triangle. If ABC is right-angled (respectively, obtuse-angled), and C
Theorem 2. Let ABC be any triangle, with a = |BC|, b = |CA|, c = |AB|, and area ∆. If XY Z is inscribed in ABC, then
|XY | + |Y Z| + |ZX| ≥ 8∆
2
abc . (1)
Equality holds in (1) if and only if ABC is acute-angled; and then only if XY Z is its orthic triangle. If ABC is right-angled (respectively, obtuse-angled), and C
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