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KVPY2012MathematicsProperties of Triangles

Let H be the orthocenter of an acute - angled triangle ABC and O be its circumcenter. Then HA + HB + HC

Options

  1. Ais equal to HO
  2. Bis equal to 3 HO
  3. Cis equal to 2 HO
  4. Dis not a scalar multiple of HO in general

Correct answer

C. is equal to 2 HO

Step-by-step solution

G is centroid array l G = A + B + C 3 G = 20+ H 3 2 O + H =3 G HA + HB + HC = A - H + B - H + C - H = A + B + C -3 H =3 G -3 H =2 O + H -3 H =2 O -2 H =2 HO array

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