InterviewSolution
Saved Bookmarks
| 1. |
If the sides of a cyclic quadrilateral are 3,3,4,4, show that a circle be inscribed in it. |
|
Answer» Solution :Since, length of tangents from EXTERNAL point to a circle are equal. `THEREFORE` AP=AS………(i) BP= BQ ……(ii) CR = CQ ………….(iii) DR=DS…………..(iv) `therefore AB+ CD = (AP + PB) (CR + DR)` `=(AS + BQ) + (CR + DS) =(AS+DS) + (BQ+CR)` `rArr AB + CD = AD + BC`.....(1) `therefore` A circle can be inscribed in a QUADRILATERA, if sides of a quadrilateral satisfies (1) Sides of quadrilateral are 3,3,4,4. If we take AB=3, CD=4, BC=3, AD=4 `therefore AB+CD = BC + AD=7` `therefore` Circle is inscribed in quadrilateral ABCD. If sum of opposite sides of a quadrilateral is equal. only then a cirlcle can be inscribed in a quadrilateral. |
|