Write-Up #8

Altitudes and Orthocenters

By Jaepil Han

Problem 6. Given acute triangle ABC. Construct the Orthocenter H. Let points D, E, and F be the feet of the perpendiculars from A,  B, and C respectfully.



(a) Prove HD/AD + HE/BE + HF/CF = 1


(b) Prove AH/AD + BH/BE + CH/CF = 2


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