# SOLUTION: you are given rectangle abcd. how many distinct circles in the same plane of the rectangle have a diameter both of whose endpoints are vertices abcd? what is the sum of the diamete

Algebra ->  -> SOLUTION: you are given rectangle abcd. how many distinct circles in the same plane of the rectangle have a diameter both of whose endpoints are vertices abcd? what is the sum of the diamete      Log On

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 Question 8853: you are given rectangle abcd. how many distinct circles in the same plane of the rectangle have a diameter both of whose endpoints are vertices abcd? what is the sum of the diameters of all of the circles? be sure to answer both questions. A-----------------------------D 5 cm. B-----------------------------C 12 cm.Answer by khwang(438)   (Show Source): You can put this solution on YOUR website! I think you mean AB = CD = 5, AD= BC = 12. Let AC and BD intersect at O, we see that AO=CO= BO=DO . [Set it be r] The circle centered at O with radius r passing through A,B,C & D. This is the unique circle (in the same plane of the rectangle) have two diameters AC & BD whose endpoints are vertices A,B,C & D. By Pyth. theorem AC^2 = AB^2 + BC^2 = 169,so AC = 13 cm (=BD). Hence, the sum the diameters = 26 cm Since there are infinitely many diamaters in circle, the question should not ask "what is the sum of the diameters of all of the circles?" in this unreasonable way. Kenny