Monday, November 11, 2019

calculus - Maximize the area of an isosceles triangle bounded by a circle

Maximize the area of an isosceles triangle (let the smallest of the triangle's three angles = $2\theta$)



Triangle is bounded by a circle with radius $R$



Find angle $\theta$ which maximizes the area of the bounded triangle



Drew this out with $2\theta$ vertex pointing upward




Drew lines from center of the circle out to each vertex and noted that the angle directly below $2\theta$ (at center of circle) = $4\theta$



Next steps: possibly finding $\sin(2\theta)$ and $\cos(2\theta)?$ Not sure where to go from here. Any help welcomed.

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