ABCD is a cyclic quadrilateral in which ab is equal to 14.4 CM BC is equal to 12.8 CM CD is equal to 9.6 if AC bisects BD then what is the length of AD
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In any cyclic quadrilateral, the ratio of the diagonals is equal to the ratio of the sums of products of the sides that share the diagonals’ end points.
In other words if AB,BC,CD, DA are the sides and AC and BD are the diagonals, then AC:BD = (AB.AD+BC.CD):(AB.BC +AD.CD). The proof of this result is based on similar triangles.
Substituting the lengths of known sides and a diagonal BD, we can find the length of the other diagonal AC.
So, AC: 221 = (204*85 + 104*195)(204*104+85*195) = (17340+20280)(21216+16575)=37620/37791.
So, AC = 37620*221/37791 =220.
AC = 220.
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