GATE 2022 MA – Question 9

General Aptitude · Quantitative Aptitude: Algebra, Geometry and Mensuration · 2 marks · Multiple choice

Letters P,Q,R,S,T,U occupy the vertices of a regular convex hexagon. RS is longer than PQ and perpendicular to PQ. RU is parallel to TQ. Which follows?

RT is parallel to QS.
TQ is parallel to PU.
RP is perpendicular to UQ.
QS is perpendicular to RP.

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Correct answer: (A) RT is parallel to QS.

Explanation

Hexagon chord lengths are side a, short diagonal √3a and diameter 2a. The given perpendicular unequal disjoint chords must be a diameter RS and a short diagonal PQ. Their endpoints leave two vertices for T,U; RU∥TQ fixes their order. Up to rotation/reflection the cyclic order is P,S,Q,U,R,T. In this order RT and QS are parallel opposite horizontal chords. **A**.

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