inscribe a rectangle of base b and height h in a circle of radius one, and inscribe an isosceles triangle in a region of the circle cut off by one base of the rectangle (with that side as the base of the triangle). for what value of h do the rectangle and triangle have the same area?
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1 answer

let the height of the triangle be y. Then since the center of the rectangle is also the center of the circle,
y + h/2 = 1
and so we have
bh = by/2
bh = b(1h/2)/2
solve for h, and use (b/2)^2 + (h/2)^2 = 1
to find b 👍
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answered by oobleck
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