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Most Important Selected Qs for JEE AdvancedMathematicsStraight Lines

A (3,4) B (0,0) and C(3,0) are vertices of A B C . If ' P ' is a point inside A B C such that d(P, B C) . d(P, A B), d(P, A C) , where d(P, B C) represents distance of P from B C , then identify correct statement -

Options

  1. Aif d ( P , BC ) is maximum, then P is incentre of the triangle.
  2. Bif d ( P , BC ) is maximum, then P is centroid of the triangle.
  3. Cd ( P , BC )=1
  4. Dd ( P , BC )= 4 3

Correct answer

C. d ( P , BC )=1

Step-by-step solution

d ( P , BC ) . d ( P , AB ), d ( P , AC ) The region represented is shown by shaded region, where BP and CP are angle bisectors Clearly maximum of d ( P , BC ) occurs, when P is incentre of ABC Maximum of d ( P , BC )= PN = ordinate of incentre P =1

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