InterviewSolution
Saved Bookmarks
InterviewSolution
| 1. |
A quadrilateral ABCD is drawn to circumscribe a circle. Prove that AB+CD=AD+BC. or A circle touches all the four sides of a quadrilateral ABCD. Prove that AB+CD=BC+DA. |
|
Answer» SOLUTION :LET the circle touches the sides AB,BC,CD and DA of a SQUAREABCD at P,Q,R and S respectively. Since, the tangents drawn from an external point to a circle are equal in length. `:.""AP=AS""...(1)` `BP=BQ""...(2)` `CR=CQ""...(3)` and`""DR=DS""...(4)` Adding (1), (2), (3) and (4), we get `ubrace(AP+BP)+ubrace(CR+DR)=AS+BQ+CQ+DS` `implies""AB+CD=(AS+DS)+(BQ+CQ)` `implies""AB+CD=AD+BC""` Hence Proved. 
|
|