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Let A≡(−4,0) and B≡(4,0) If the number of points on the circle x2+y2=16 such that the area of the triangle whose vertices are A, B, and C is a positive integer N then the value of N is __________

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answer is 62.

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Detailed Solution

Required areaA=12×8×4sinθ=16sinθNow, the area is an integer. Then the possible values of sinθ are116,216,…,1516 i.e., 15 points in each quadrant or 60 + 2 more with sin θ =1Therefore, N=62

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Let A≡(−4,0) and B≡(4,0) If the number of points on the circle x2+y2=16 such that the area of the triangle whose vertices are A, B, and C is a positive integer N then the value of N is __________