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The quadrilateral circumscribed about a circle can be divided into four triangles. Radii of circle drawn to points of tangency are altitudes of a triangles. The area of quadrilateral is sum of areas of these triangles. A = 1/2 * a * r + 1/2 * b * r + 1/2 * c * r + 1/2 * d * r / * 2, 2A = ar + br + cr + dr, 2A = r(a+b+c+d)/:(a+b+c+d), r = 2A / (a + b + c + d).