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?
Explanation:
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).
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