Saturday, May 1, 2010

Fox 280


  1. divide
    answer is 2

  2. Newzad, I wonder how you got to x=2 so quickly! I had to solve the following equation to get to it: If the original triangle is ABC with A=2α+β, B=β & C=α then after constucting a line CD making an angle of α with AC and meeting BA extended in D, we can write from triangles ABC & DBC:((x(2x+3)/(x+2))^2 + (x+2)^2 -(x+1)^2)/(2(x+2)( x(2x+3)/(x+2)))=(-(x+1)^2+x^2+(x+2)^2)/(2x(x+2)) both being =cos(β). This gives x=2.
    Rather a long derivation! Is there any shorter way possible?

  3. DRAW A LINE FROM TOP to base that divide the angle a and there exist a isosceles triangle where congruent side is there are two similar(a.a) triangles x+1,x+2,1 and 1,x,y. so x=2

    1. Please if you want write more about that solution.

  4. My solution is same with Narziss's one. So i didn't explained,sorry
    Thanks Narziss

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