Saturday, April 7, 2012

Fox 351

Let's start with this simple one for high-schoolers :)
Pure-geometric solution will be appreciated.
We'll build upon this later.


  1. jyu

  2. Question rephrased as :-

    Given that PQR is an equilateral triangle. M and N are points on PQ and PN respectively such that PM = a and PN = b.

    Construction : (1) Draw NH//RQ cutting PQ at H.
    (2) Draw MK perpendicular to NH produced and meeting it at K.

    Proof :-
    PNH is an equilateral triangle of side b.
    MH = a - b.
    HK = c - b.
    MHK is a special triangle with <MHK = 60 degrees
    Hence, MH : HK = 2 : 1
    result follows

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