Question

Calculus: Can anyone explain how to solve this? (Or link a video or website that will... I've got a final in like 30 minutes -_-)
Find the smallest possible area of an isosceles triangle that is circumscribed about a circle of radius r.

Thanks a bunch!

Answer 1

First you probably want to find a relationship between the the height and the radius (ie get h in terms of r). Then try to get some form of the base in terms of radius, then use half base*height for the triangle area, and differentiate it to minimize the area.

Answer 2

Thanks for your response @agent0smith, but the circle is inside the triangle >_< lol

Answer 3

im pretty sure smallest area would be an equilateral triangle
in whic case :

Area = 3sqrt3 r^2

Answer 4

@dumbcow Thanks, I know the answer (this is an odd numbered question in our textbook lol) but I wanted to know how to go about solving it...

Answer 5

yeah i figured..hold on im working it out
you need to relate base and height in terms of "r"
then minimize Area by setting derivative equal to 0

Answer 6

sorry its taking so long...its getting messy
i guess you couldn't start off by assuming its an equilateral triangle could you?

Answer 7

xD I guess not. Thank you for trying to help though. There is a video tutorial for my textbook, but its ridiculous. It starts by drawing the image, then does a vertical line down the center of the triangle, then a line the size of the radius of the circle to the side of the triangle to make two right tangles, then it finds that the side above the angel is sqrt (x^2+2rx) but I really don't understand it - it was only confusing me more so I just shut the video off. I've got to leave now though, maybe if I'm early enough I can have the professor explain it... or something >.<