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Math Help - Calculus .. Area Question

  1. #1
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    Calculus .. Area Question

    An isosceles triangle is inscribed in a circle with radius one metre in such a way as to
    maximize the area of the triangle. Determine its area. (Hint: Consider the area as a
    function of the distance from the centre of the circle to the base of the triangle)
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  2. #2
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    Quote Originally Posted by sam126 View Post
    An isosceles triangle is inscribed in a circle with radius one metre in such a way as to
    maximize the area of the triangle. Determine its area. (Hint: Consider the area as a
    function of the distance from the centre of the circle to the base of the triangle)
    What have you tried? Where are you stuck?
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  3. #3
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    Area = \frac{base\cdot height}{2}

    If the distance to the base from the center of the circle is r, then the height of the triangle is h=r+1 since the radius of the circle is 1 and we assume that all corners of the triangle touch the circle. All the corners of the triangle will be at the distance r=1 from the center of the circle, so the base is going to have the length \frac{b}{2}=\sqrt{1-r^2}

    So we have Area = \frac{base\cdot height}{2}=(1+r)\sqrt{1-r^2}
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