Question 57270
givin three sides of a traingle: 330, 270, 240, find the area of the largest possible circle that fits within the triangle
givin three sides of a traingle: 330, 270, 240, find the area of the largest possible circle that fits within the triangle

SUCH A CIRCLE IS CALLED INCIRCLE.THERE ARE SEVERAL WAYS TO FIND IT.I DONOT KNOW ABOUT 
YOUR BACK ROUND. I AM GIVING BELOW ONE WAY USING TRIGNOMETRY - PROPERTIES OF TRIANGLES.

DEL = r*s = SQUARE ROOT OF [ s(s-a)(s-b)(s-c)]
WHERE 
DEL = AREA OF TRIANGLE
r = IN RADIUS
a,b,c ARE SIDES OF TRIANGLE
s = (a+b+c)/2 = SEMI PERIMETER OF THE TRIANGLE.
WE HAVE 
a = 330
b = 270
c = 240
s = (a+b+c)/2 = (330+270+240)/2 = 840/2 = 420
r*420 = SQ.RT.[420(420-330)(420-270)(420-240)] = 					31946.83083
r*420 = 31947					
r = IN RADIUS = 31947/420 = 			76.06388095		
AREA OF INCIRCLE = PI*r*r = 			18167.19878