The chord of the contact of tangents drawn from a point on the circle x2 + y2 = a2 to the circle x2 + y2 = b2 touches the circle x2 + y2 = c2 such that bp = amcn , where m, n, p, ? N, and m, n, p are prime to each other, then the value of 2m + n + 2p – 3 is:
Show answer & explanation
Correct answer: D
Explanation
Correct Answer is option 4 i.e. 4
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Understanding |
Application |
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Given, x2 + y2 = a2 (Biggest) x2 + y2 = b2 x2 + y2 = c2 (Smallest) are three circles of radius a, b, c.
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According to the figure: OC = c, OB = b, OA = a, OD = b In triangle OAD: AD = √(OA2 – OD2) = √(a2 – b2) In triangle OCD: AD = √(OD2 – OC2) = √(b2 – c2) In triangle ACD: AD2 = AC2 + CD2 a2 – b2 = a2 + c2 – 2ac + b2 – c2 - b2 = - 2ac + b2 - 2b2 = -2ac b2 = ac On comparing with bp = amcn We get, p = 2, m = 1, n = 1 So, 2m + n + 2p - 3 = 2 × 1 + 1 + 2 × 2 - 3 = 4 |
