three circles with same radius r are drawn with centres as
three vertices of a triangle.what is the sum of areas of the
intersections of these circles with the triangle
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Answer Posted / andrew
PROVIDING the radius of the circle is smaller than any of
the sides of the triangle, and smaller than any of the
perpendicular distances from corner to opposite side, the
answer will be that as stated in Answer #1 above...
sum of the internal angles of the triangle is 180degrees.
This means that half the area of one of the circles will be
within the triangle... so half the area of the circle can
be calculated as 0.5 * pi * radius * radius.
IF the radius is sufficiently large in comparison to the
triangle, the sum of the areas will tend towards a maximum
of the area of the triangle itself.
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