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MHT CET202615 April 2026Evening ShiftMathematicsProperties of TrianglesActual

In a triangle ABC, with the usual notations, B = 3 , C = 4 . If D divides BC internally in the ratio 1:3, then BAD CAD =

Options

  1. A1 3
  2. B1 3
  3. C1 6
  4. D2 3

Correct answer

C. 1 6

Step-by-step solution

Let BAD = and CAD = . Applying the sine rule in ABD : BD = AD B BD = AD B Applying the sine rule in ACD : CD = AD C CD = AD C Dividing the two equations: BD CD = C B Rearranging for the required ratio: = BD CD B C Given that D divides BC internally in the ratio 1:3 , we have BD CD = 1 3 . Also given B = 3 and C = 4 . Substituting these values: = 1 3 ( 3 ) ( 4 ) = 1 3 3 2 1 2 = 1 3 3 2 = 1 6 Answer: 1 6

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