Saved Bookmarks
| 1. |
Example 14: O is any point inside arectangle ABCD (see Fig. 6.52). Prove that |
|
Answer» Let ABCD be the given rectangle with point O within it. Join OA, OB, OC, OD. Through O draw EOF||AB.Then ABFE is a rectangle.In right ∆OEA and ∆OFC,OA² = OE² + AE² and OC²= OF²+CF²OA²+OC²=(OE²+AE²) +(OF²+CF²)OA²+OC²=OE²+OF²+AE²+CF²………….(1)In right ∆OFB and ∆ODE,OB² = OF² + FB² and OD²= OE²+DE²OB²+OD²=(OF²+FB²) +(OE²+DE²)OB²+OD²=OE²+OF²+DE²+BF²OB²+OD²=OE²+OF²+CF²+AE²…………..(2)[DE=CF & AE=BF]From eq i & eq ii,OA² + OC² = OB² + OD² HOPE THIS WILL HELP YOU |
|