A link between sectors and radius
Circles A and B have the same area and are overlapping. A vertical and straight line is drawn between the two points at which the circumferences of the circles intersect, and we shall call this line PQ. Another line is drawn between the points of each circle's circumference that reach deepest into the other circle and we shall call this line M. Line PQ has length 6cm, M has length 8cm and they are both perpendicular to each other. Find one of the circumferences of the circles (Round off answer to the nearest tenth).
The answer is 19.6.
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1 solution
Say Line PQ/2 = b
and Line M/2 = a
If you draw a line of radius to either point P or Q, you will see that
b^2 = r^2 - (r-a)^2
Hence,
b^2 + a^2 = 2ar - a^2 + a^2 = 2ar
(b^2 + a^2)/a = 2r
Input the values:
b = 3
a = 4
(3^2 + 4^2)/4 = 25/4 = 6.25
2 * pi * r = 6.25 * pi = 19.6
Therefore, the circumference of each circle is 19.6 cm.
Sorry about the horrible formatting though... my keyboard is broken so it's messing up the signs...