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AP EAMCET201822 Apr 2018Morning ShiftMathematicsProperties of TrianglesActual

If the median of a A B C through A is perpendicular to A C , then A C =

Options

  1. A1+ 2
  2. B- 1 3 +1
  3. C-2
  4. D1+ 2 3

Correct answer

C. -2

Step-by-step solution

A B C is the triangle while A M is the median A C and A M are perpendicular. M A C=90^ Since, A M is the median, M is the mid-point of line B C . B M=C M=2 B C Draw a line perpendicular to A M (through M ) let it intersect the line A B at P . In A B C , A+ B+ C=180^ In A M C , array rlrl & A M C+ C A M+ M C A & =180^ & & A M C+90^ + C & =180^ & A M C & =90^ - C array Again at point M . array rlrl & & B M P+ P M A+ A M C & =180^ & B M P+90^ +90^ - C & =180^ & & B M P & = C array But in B P M , aligned & B P M+ B M P

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