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KVPY2016MathematicsStraight Lines

Let P be a point inside a triangle ABC with ABC =90^ . Let P ₁ and P ₂ be the images of P under reflection in AB and BC respectively. The distance between the circumcenters of triangles ABC and P ₁ P P ₂ is

Options

  1. AAB 2
  2. BAP + BP + CP 3
  3. CAC 2
  4. DAB + BC + AC 2

Correct answer

C. AC 2

Step-by-step solution

M is circumcentre of ABC M ( a 2 , b 2 ) & ~N is circumcentre of ABC N =(0,0)= B ( . Mid-point of . P ₁, & P ₂ ) So MN = AC 2

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