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how to solve timus 1953 ?
By problem-solved, 13 years ago, In English

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13 years ago, hide # |
 
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You need to inscribe the Steiner inellipse.

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    13 years ago, hide # ^ |
     
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    I read about Steiner inellipse but i don't figure out how to solve that problem. Triangle's area could be found by Heron formula and the Elipse area is pi/(3 sqrt(3)) of that one. Elipse area beside could be calculated as pi*a*b where a is major semi-axis and b minor semi-axis. Steiner inellipse say that the elipse is tangent at the middel point of the three sides. The center of the Elipse is the baricenter of the triangule.

    Please help. Thanks

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13 years ago, hide # |
 
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I can teach you my dear ~~~~^_^

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13 years ago, hide # |
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You can use coordinate transformation to get equilateral triangle from the given, and according to sample the answer for equilateral triangle is circle. As I remember, this task or similar was discussed in CF recently.

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There is a way to find focuses of Steiner ellipse: Marden's_theorem. After that you can find R, for example, from this fact: Steiner ellipse is tangent to the sides of triangle at their midpoints. Simply put midpoint of any side into ellipse equation.

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