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One side of a triangle is divided into segments of length a and b by the inscribed circle, with radius r. Prove that the area is: abr(a+b)/ab-r^2

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Strange Rectangle 2

Find the exact values of some trig. ratios from this rectangle in which a cyclic quadrilateral cuts off four right angled triangles.

Shape and Territory

Stage: 5 Challenge Level: Challenge Level:1

If for a triangle $ABC$

$\tan(A - B) + \tan(B - C) + \tan(C - A) = 0$

what can you say about the triangle?