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AP EAMCET201726 Apr 2017Morning ShiftMathematicsProperties of TrianglesActual

If , , are the lengths of the tangents from the vertices of a triangle to its incircle. Then

Options

  1. A+ + = 1 r^2 ( )
  2. B1 + 1 + 1 =r( )
  3. C+ + = 1 r ( )
  4. D^2+ ^2+ ^2= 2 r ( )

Correct answer

A. + + = 1 r^2 ( )

Step-by-step solution

It is given that , , are the length of tangents from the vertices of a triangle to its incircle. Semi-perimeter of A B C , aligned S= + & + Area of A B C & = s(s-a)(s-b)(s-c) & = ( + + )( )( )( ) aligned As we know, aligned & r= / s & r= ( + + )( ) + + & r^2= ( + + )( ) ( + + )^2 & Hence, + + = r^2 aligned

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