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## Perpendiculars from Center (Tomato subjective 107)

Problem : If a, b and c are the lengths of the sides of a triangle ABC and  if $$p_1 , p_2$$ and $$p_3$$   are the lengths of the perpendiculars drawn from the circumcentre onto the sides BC, CA and AB respectively, then show that . Solution : Let  O be the circum...

## Sum of polynomials (Tomato subjective 173)

Problem : Let be polynomials in , each having all integer coefficients, such that . Assume that is not the zero polynomial. Show that  and  Solution : As are integer coefficient polynomials so gives integer values at integer points. Now as is not zero polynomial for...

## Round robin tournament (Tomato subjective 172)

Problem : Suppose there are teams playing a round robin tournament; that is, each team plays against all the other teams and no game ends in a draw.Suppose the team loses games and wins games.Show that = Solution : Each team plays exactly one match against each other...