ρ b D d
نویسنده
چکیده
Fig. 1 Let ABCD be a circumscribed quadrilateral, that is, a quadrilateral which has an incircle. Let this incircle have the centerO and the radius ρ and touch its sides AB, BC, CD, DA at the points X, Y, Z, W, respectively. Then, for some very obvious reasons, OX ⊥ AB, OY ⊥ BC, OZ ⊥ CD, OW ⊥ DA and OX = OY = OZ = OW = ρ. Moreover, AW = AX, BX = BY, CY = CZ, DZ = DW, since the two tangents from a point to a circle are equal in length. We denote a = AW = AX; b = BX = BY ; c = CY = CZ; d = DZ = DW. (Thus, we denote by a, b, c, d not, as usual, the sidelengths of the quadrilateral ABCD, but the segments AW = AX, BX = BY, CY = CZ, DZ = DW.) Then, the sidelengths of quadrilateral ABCD are AB = AX +BX = a+ b; BC = BY + CY = b+ c; CD = CZ +DZ = c+ d; DA = DW + AW = d+ a. 1I am grateful to George Baloglou for correcting a mistake in Theorem 13.
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