2. Sample Papers
  3. JEE Main & Advanced

JEE Main & Advanced Sample Paper JEE Main - Mock Test - 40

  • question_answer
    In \[\Delta ABC,\] I is the in centre. Areas of \[\Delta IBC,\] \[\Delta lAC\] and \[\Delta lAB\] are, respectively, \[{{\Delta }_{1}},{{\Delta }_{2}}\] and\[{{\Delta }_{3}}\]. If  \[{{\Delta }_{1}},{{\Delta }_{2}}\]and \[{{\Delta }_{3}}\] are in A.R, then the altitudes of \[\Delta ABC\]are in

    A) A.P.

    B)        G.P.

    C) H.P.

    D)        None of these

    Correct Answer: C

    Solution :

    [c] \[{{\Delta }_{1}}=\frac{1}{2}ra,\]   \[{{\Delta }_{2}}=\frac{1}{2}rb,\] s\[{{\Delta }_{3}}=\frac{1}{2}rc\] \[{{\Delta }_{1}},{{\Delta }_{2}},{{\Delta }_{3}}\]are in  A.P. So, a, b, c are in A.P. Let A be the area and x, y, z be the altitudes of the triangle ABC. Then \[x=\frac{2\Delta }{a},\,y=\frac{2\Delta }{b},\,z=\frac{2\Delta }{c}\] Hence, x, y, z are in H.P.           


You need to login to perform this action.
You will be redirected in 3 sec spinner