Question 57270: givin three sides of a traingle: 330, 270, 240, find the area of the largest possible circle that fits within the triangle
Answer by venugopalramana(3286)   (Show Source):
You can put this solution on YOUR website! 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
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