Iron man mark 1 (43 to go) series of challenges for geniuses

Geometry Level 4

Suppose a line 'l' cuts an equilateral triangle A B C ABC of side 3 \sqrt{3} in two points different from the vertices. Say it cuts A B AB and A C AC in points R R and Q Q respectively. We mark the orthocentre H H of the triangle A R Q ARQ and also the midpoint M M of side R Q RQ . We extend H M HM to a point T T so that H M = M T HM = MT . The point P P is the foot of perpendicular from T T on side B C BC .

Now, we draw outward equilateral triangles R A Q RA'Q , Q C P QC'P , and P B R PB'R . (The Napoleonic triangles of triangle P Q R PQR ).

The task is to find: A T + B T + C T A'T + B'T + C'T .


The answer is 3.0.

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1 solution

Hrisheek Yadav
Dec 11, 2015

( 4 / 6 ) Ψ = 02 / 3.3 / 2 = U n i t y 3 Υ = 3 (4/6)\Psi =02/3.3/2=Unity 3\Upsilon =3

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