The lengths of three consecutive sides of a quadrilateral circumscribing a circle are 4 cm, 5 cm and 7 cm respectively. Determine the length of the fourth side.
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The length of the fourth side = 6 cm.
Let ABCD be a quadrilateral with sides AB = 4 cm, BC = 5 cm, CD = 7 cm and DA = x circumscribing a circle at points E, F, G and H.
Consider the figure, while going through the following steps.
As the tangents drawn from an external point to the same circle are of equal length, we have,
AE = AH
BE = BF
CG = CE
DG = DH
Adding above all the equations, we have,
AE + BE + CG + DG = AH + BF + CE + DH
AB + CD = AD + BC
4 + 7 = x + 5
11 = x + 5
x = 11 - 5
x = 6 cm
DA = 6 cm.
The length of the fourth side = 6 cm.
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