2. Solved Papers
  3. 10th Class
  4. Mathematics

10th Class Mathematics Solved Paper - Mathematics 2017 Outside Delhi Set-I

  • question_answer
    A circle touches all the four sides of a quadrilateral ABCD. Prove that \[AB+CD=BC+DA\]

    Answer:

    Given, a quad. ABCD and a circle touches it?s all four sides at P, Q, R, and S respectively.
    To prove:           \[AB+CD=BC+DA\]
                               L.H.S.    \[=AB+CD\]
             \[=AP+PB+CR+RD\]
             \[=AS+BQ+CQ+DS\]
    (Tangents from same external point are always equal)
             \[=(AS+SD)+(BQ+QC)\]
             \[=AD+BC\]
             = R.H.S.              Hence Proved.


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