Saved Bookmarks
| 1. |
If a, b and c are sides of a right-angled triangle wherec is the hypotenuse. Prove that radius r of the circlewhich touch the sides of the triangle is given byr=a +b-c/2 |
|
Answer» Let the circle touches the sides BC, CA, AB of the right triangle ABC(right angled at C) at D, E and F respectively, where BC= a, CA=b , AB= c respectively Since lengths of tangents drawn from an external point are equal Therefore, AE=AF, and BD=BF Also CE=CD=r and b-r=AF , a- r= BF Therefore AB=AF+BF c= b-r + a-r AB=c=AF+BF=b-r+a-r hence, r=a+b-c/2 |
|