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XAT 2020 — QA & DI Question 20

Basics of CirclesEasy

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?

Answer & solution

  • A

    XZ + YP = XY + PZ

  • XP = YP + PZ

  • C

    XP + PZ = XY + YP

  • D

    XP = XY

  • E

    XP = XY + YZ

Solution

​​​​​​​

Ptolemy’s theorem:
Product of diagonal of a cyclic quadrilateral is equal to sum of product of opposite pair of sides.

∴ XP × YZ = PY × XZ + PZ × XY

⇒ XP × a = PY  × a + PZ × a

⇒ XP = PY + PZ

Hence, option (b).

XAT 2020 QA & DI Q20: XYZ is an equilateral triangle, inscribed in a circle. P is a point on the arc YZ such that X and P are on opp — Solution | TheCATExam