Equality in a triangle

Geometry Level 2

Given an acute triangle ABC. Draw a point D, E, F on each side of triangle ABC such that AD, BE and CF are the altitudes, which intersect each other at H. Calculate:

H D A D + H E B E + H F C F \frac{HD}{AD} + \frac{HE}{BE} + \frac{HF}{CF}

(All the name of each side of a triangle in the equation above refer to its length).


The answer is 1.

Tin Le by Tin Le , 15, Vietnam

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1 solution

Nemesis Coming
Jun 12, 2019

Take a special case of equilateral triangle and d,e,f points should be medians

Then HD/AD=1/3

Same way all sides

0 Helpful 0 Interesting 0 Brilliant 0 Confused

The answer is always 1 no matter what kind of the triangle it is.

Tin Le - 1 year, 12 months ago

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