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Get access to the detailed solutions to the previous year's questions asked in XAT exam.
If we join YP and PZ, XYPZ will become a cyclic quadrilateral. YZ and XP will be diagonals of this quadrilateral.
Ptolemy's theorem states that the product of the length of the diagonals is equal to the sum of products of measures of the pairs of opposite sides.
As per this theorem for the quadrilateral :
XY*PZ +XZ*PY = YZ*XP.
For the equilateral triangle.
Now, in equilateral triangle XYZ, YZ = XZ = XY.
Hence equation 1 becomes, XP = YP + PZ.