Saved Bookmarks
| 1. |
A triangle has sides of length 6, 7 and 8. The line through its incenter parallel to the shortestside is drawn to meet the other two sides at P and Q. The length of the segment PQ is |
|
Answer» `12/5`  Let AD=h , ID=x AREA of triangle ABC=R.s `=r((6+7+8)/2)` `=21/2r` …(1) Area of triangle `ABC=1/2BCxxh` `=1/2(6)xxh=3h` …(2) From (1) and () `"2lr"/2=3h` `r/h=6/21=2/7` TriangleABC and triangle APQ are similar `therefore (PQ)/(BC)=(h-r)/h` `(PQ)/6=1-r/h` `(PQ)/6=1-2/7` `rArr PQ=30/7` |
|