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Q.

Let the distance between two parallel lines be 5 units and a point P 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 R lies on the other. Then (QR)2 is equal to ________. 

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answer is 28.

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Detailed Solution

Question Image

PR = cosecθ, PQ = 4sec(30 + θ) 
For equilateral
d = PR = PQ
⇒cos⁡θ+30∘=4sin⁡θ⇒32cos⁡θ−12sin⁡θ=4sin⁡θ⇒tan⁡θ=133QR2=d2=cosec2θ=28

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