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KVPY2016MathematicsProperties of Triangles

Let AB be a sector of a circle with centre O and radius d, AOB = ( < 2 ) , and D be a point on OA such that BD is perpendicular OA . Let E be the midpoint of BD and F be a point on the arc AB such that EF is parallel to OA . Then the ratio of length of the arc AF to the length of the arc AB is -

Options

  1. A1 2
  2. B2
  3. C1 2
  4. D⁻¹ ( 1 2 )

Correct answer

D. ⁻¹ ( 1 2 )

Step-by-step solution

CF = r (1- ) EC = r ( - ) CD = r EC + CD = ED r = r 2 = ⁻¹ ( 2 )

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