Saved Bookmarks
| 1. |
(b) ABCD is a quadrilateral in which the diagonals AC and BD intersect at 0. Prove thatAB+BC + CD + AD < 2(AC + BD).hc |
|
Answer» Who was the wrote biology book ABCD is a quadrilateral and AC, and BD are the diagonals. Sum of the two sides of a triangle is greater than the third side. So, considering the triangle ABC, BCD, CAD and BAD, we getAB + BC > AC ..........(1)CD + AD > AC .........(2)AB + AD > BD .........(3)BC + CD > BD .........(4) Adding all the above equations, 2(AB + BC + CA + AD) > 2(AC + BD)⇒ 2(AB + BC + CA + AD) > 2(AC + BD)⇒ (AB + BC + CA + AD) > (AC + BD)⇒ (AC + BD) < (AB + BC + CA + AD) |
|