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KVPY2012MathematicsProperties of Triangles

In triangle ABC , let AD , BE and CF be the internal angle bisectors with D, E and F on the sides BC , CA and AB respectively. Suppose AD , BE and CF concur at I and B , D , I , F are concyclic, then IFD has measure -

Options

  1. A15^
  2. B30^
  3. C45^
  4. DAny value 90^

Correct answer

B. 30^

Step-by-step solution

array l AIC =180^ - ( A + C 2 ) =180^ - ( A + C 2 ) =90+ B 2 array Here :-90+ B 2 + B =180^ B =60^ This will be case of equilateral IFD =30^

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