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MHT CET202527 Apr 2025Evening ShiftMathematicsProperties of TrianglesActual

In a triangle A B C , with usual notation, B= / 3, C= / 4 . D divides B C internally in the ratio 1:3 then BAD CAD

Options

  1. A(x dy d x - y )^2
  2. B( y d x dy -x )^2
  3. C(x dy d x + y )^2
  4. D( y d x dy +x )^2

Correct answer

A. (x dy d x - y )^2

Step-by-step solution

Let BAD = and CAD = . Given B = 3 = 60^ and C = 4 = 45^ in ABC , with point D dividing BC in ratio BD:DC = 1:3 . Applying the Sine Rule In ABD : BD = AD B , so BD = AD B . In ACD : DC = AD C , so DC = AD C . Using the given ratio Since BD DC = 1 3 : AD B AD C = 1 3 → C B = 1 3 Solving for the required ratio = 1 3 B C = 1 3 60^ 45^ = 1 3 3 2 1 2 = 6 6

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