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Altitudes and Orthocenters

By

B.J Kim

 

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

 

To prove the first part, I examine the area of the triangle above.

We can know the area of the triangle ABC

 

Now, Let's go to the 2nd proof