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Topic: Three half-circles
Replies: 4   Last Post: Sep 6, 2011 8:51 PM

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Rouben Rostamian

Posts: 193
Registered: 12/6/04
Re: Three half-circles
Posted: Sep 4, 2011 12:45 PM
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> Let DEF be a rectangular triangle such that D=[0 0
> 0], E=[3 0 0] and F=[0 4 0]. On the sides DE, DF and
> EF are constructed respective half-circles with
> positive z-axis and perpendicular to the xy-plane.
> Determine the parameters A, B, C of the plane A*x +
> B*y + C*z = 1 , that tangents the three
> half-circles.


Hello Avni, thanks for this interesting puzzle.
I obtained A = -3/16, B = -4/9, C = 5/6. I did not attempt for a "clever" solution; I just wrote down the parametric equations of the three circles, then wrote down the conditions of their tangency to the plane, and solved the resulting system of six equations in six unknowns.

Rouben



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