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AP EAMCET201726 Apr 2017Morning ShiftMathematicsThree Dimensional GeometryActual

In A B C, ~L , M , N are points on B C, C A, A B respectively, dividing them in the ratio 1: 2,2: 3,3: 5 . If the point K divides A B in the ratio 5: 3 , then

Options

  1. A5 8
  2. B2 5
  3. C3 5
  4. D1 15

Correct answer

D. 1 15

Step-by-step solution

Given that, in A B C, L, M, N are points on BC, CA and AB respectively, dividing in the ratio 1: 2,2: 3 and 3: 5 . Also, point K divides A B in the ratio 5: 3 . Now, according to the section formula, aligned & L= 2 b + c 3 , M= 2 a +3 c 5 & N= 3 b +5 a 8 , K= 5 b +3 a 8 & AL = 2 b + c 3 - a = 2 b + c -3 a 3 & BM = 2 a +3 c 5 - b = 2 b +3 c -5 b 5 & CN = 3 b +5 a 8 - c = 3 b +5 a -8 c 8 & CK = 5 b +3 a 8 - c = 5 b +3 a -8 c 8 & AL + BM + CN CK = aligned aligned & | 2 b + c -3 a 3 + 2 a +3 c -5 b 5 + 3 b +5 a -8 c 8

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