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Two poles of height 10 meters and 20 meters stand at the centres of two circular plots which touch each other externally at a point and the two poles subtend angles 3 0 o and 6 0 o respectively at this point, then the distance between the centres of these circular plots is

Options

  1. A30 meters
  2. B50 3 meters
  3. C70 3 meters
  4. D10 3 + 20 meters

Correct answer

B. 50 3 meters

Step-by-step solution

Let, A and B be the centres of the two circles where the poles of height 10 m and 20 m respectively stand making angles 3 0 o and 6 0 o respectively at the point O where these circles touch each other externally. The sum of the radii of the two circles = The distance between the centres of the two circles. = 10 cot ⁡ 30 o + 20 cot ⁡ 60 o = 10 3 + 20 3 = 30 + 20 3 meters

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