Please enter the following details
Free Daily Targets & Mocks
Study Material & Formulas PDFs
1 on 1 Mentorship
Question 17
XYZ is an equilateral triangle, inscribed in a circle. P is a point on the arc YZ such that X and P are on opposite sides of the chord YZ. Which of the following MUST always be true?
Solution
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.
Video Solution
XAT Quant Questions | XAT Quantitative Ability
XAT Functions, Graphs and Statistics QuestionsXAT Data Sufficiency QuestionsXAT Quadratic Equations QuestionsXAT Number Systems QuestionsXAT Inequalities Questions
XAT DILR Questions | LRDI Questions For XAT
XAT Selection With Condition QuestionsXAT Truth Lie Concept QuestionsXAT Quant Based DI QuestionsXAT DI with connected data sets QuestionsXAT Charts Questions
