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Convex quadrilateral ABCD has an incircle (that is, there is a circle that is tangent to every side). Let a, b, c, and d be the lengths of the tangents from the vertices to the circle, as shown. Prove that 

\([ABCD]^2 = (a + b + c + d)(abc + abd + acd + bcd)\).

 

I haven't been able to do much but I was able to say that \(r^2(a+b+c+d) = abc + abd + acd + bcd\)

 Aug 16, 2020
 #1
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If you let a = b = c = d, then you get a square, and the formula works.

 Aug 16, 2020
 #2
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I do not understand what a,b,c and d are.

Where is the picture?

 Aug 17, 2020
 #3
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This

 Aug 17, 2020

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