If a quadrilateral has an inscribed circle then the sum of a pair of opposite sides equals ........

Quantitative Aptitude (CDS) Mensuration 2D

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If a quadrilateral has an inscribed circle, then the sum of a pair of opposite sides equals

Half the sum of the diagonals

Sum of the other pair of opposite sides

Sum of two adjacent sides

None of the above

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Explanation:

As DX and DP are pair of tangent from D to circle and we know that length of pair of tangent be same in this case.
So, Let DX = DP = 5 cm
Similarly,
Let CX = CY = 8 cm
BY = BZ = 9 cm
AP = AZ = 7 cm
Now, According to question
BD = 9 + 8 = 17 cm
AC = 7 + 5 = 12 cm
AC + BD = 17 + 12 = 29 cm
Also,
AB + CD = 29 cm
Hence the sum of a pair of opposite side equals to sum of the other pairs of opposite sides.