Two poles of height a meters and b meters stand at the centres of two circular plots which touch each other externally at a point and the two poles subtend angles of 30 o and 60 o respectively at this point, then the distance (in meters) between the centres of these plots is

Step-by-step solution

Let A and B be the centres of the two circles where the poles of height a and b respectively stand making angles 30 o and 60 o respectively at the point O where these circles touch each other externally. Sum of the radii of the two circles = a cot 30 o + b cot 60 o = a 3 + b 3 = 3 a + b 3 = distance between the centres of the two circles.