optimization questions to get ready for a test

NogardMX

I was doing some optimization questions to get ready for a test. I came across one that stumped me. The question was "Find the dimensions of the isosceles triangle of the largest area that can be inscribed in a circle of radius r".

My approach was:
let y be the base of triangle
let x be the two equal sides of triange.

A(t) = (bh)/2
= (y*(x^2-(y/2)^2)^1/2))/2

I cant find the equation to relate the radius to the area. help?

matt grime

Let the angle between the two longer sides be t, now imagine instead of drawing lines from the short edge's ends to the perimeter, you drew the lines to the centre of the circle, the angle these shorter sides (of length r) create would be 2t. There is a formula for finding the area in terms of sides and angles between sides, and t depends on the lengths chosen originally. This might help you.

NogardMX

What do you mean by "now imagine instead of drawing lines from the short edge's ends to the perimeter, you drew the lines to the centre of the circle, the angle these shorter sides (of length r) create would be 2t. "?

the formula for the area in terms of the sides of a triangle is

(s(s-a)(s-b)(s-c))^1/2

where s is (a+b+c)/2
and a,b,c are the side lengths.

is that it?