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Equilateral triangle with one vertex between two parallel lines and the other two on them

The same question, asked 2 times: 22 Jan 2025*, 21 Jan 2026 S1. Every wording below, oldest first.

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  1. Question 1

    22 Jan 2025

    148
    Let the distance between two parallel lines be 5 units and a point PP lie between the lines at a unit distance from one of them. An equilateral triangle PQR is formed such that Q lies on one of the parallel lines, while RR lies on the other. Then (QR)2(QR)^{2} is equal to ____\_\_\_\_
  2. Question 2

    21 Jan 2026 S1

    54
    Let a point A lie between the parallel lines L1L_{1} and L2L_{2} such that its distances from L1L_{1} and L2L_{2} are 6 and 3 units, respectively. Then the area (in sq. units) of the equilateral triangle ABC , where the points B and C lie on the lines L1L_{1} and L2L_{2} respectively, is :

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