look at half the center 3rd
it is a sector of the circle, with right triangles on either side
the area of the sector is
... π * r^2 * (Θ/360)
... Θ being the central angle
the combined area of the two triangles is ... r sin(Θ/2) * r cos(Θ/2) = r^2 tan(Θ/2)
π r^2 / 6 = r^2 [tan(Θ/2) + (π Θ / 360)]
π / 6 = tan(Θ/2) + (π Θ / 360)
solve for Θ
the distance from the center to the edge of the middle 3rd is
... r sin(Θ/2)
My problem is this:
Three friends want to share a circular 14-inch pizza equally by exactly only two parallel cuts. How far from the center must the cuts be? Hint: The pizza is a circle of radius 7 inches.
My professor wants a neat and detailed solution but I don't know how to even begin to go about solving this, and things that I have seen online haven't helped me in the slightest
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