Question

a circle touches the sides BC, CA, AB of triangle ABC at points D, E, F respectively BD=x, CF=y, AF=z prove that the area of triangle ANC= √xyz(x+y+z)​

Answer 1

Step-by-step explanation:

From the graph, we can see that AF = AE = z , BD = BF = x , CD = CE = y . The reason for this is that all of them are tangents of the circle.

So, the triangle ABC has sides x+z , x+y , y + z .

Now, use Heron's Formula , Area = √p(p-a)(p-b)(p-c) , where p = (a+b+c)/2

p = ( x+z + x+y + y + z ) / 2 = x+y+z

so, p -a = y , p-b = z , p-c = x

Area = √(xyz)(x+y+z)