Let be a triangle with altitudes and inradius

MATHEMATICS · Subjective · A Level · Mathematics · Algebra and Functions · Algebra and Functions

Problem

Let ABCABC be a triangle with altitudes h1,h2,h3h_1,h_2,h_3 and inradius rr. Prove that h1+rh1−r+h2+rh2−r+h3+rh3−r≥6.\frac{h_1+r}{h_1-r}+\frac{h_2+r}{h_2-r}+\frac{h_3+r}{h_3-r}\geq6.

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