XAT 2020 Question 64
This is a detailed step-by-step solution for XAT 2020 Question 64. Understand the concept, common mistakes, and expert tips to solve similar questions in XAT exam.
XAT
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.