Dynamic Geometry: P4
The diagram shows two green lines forming an angle called
, with
. We draw a cyan circle tangent to the green lines. The center of this circle must always be one unit away from the angle's apex. As
varies from
to
and back from
to
, the center of the circle moves along a pink curve. What is the ratio between the maximum perimeter of the blue circle and the lenght of the pink curve?
The answer is 2.
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1 solution
At maximum perimeter of the blue circle, the blue and the pink have the same, shared radius. As a circle is two semicircles of the same radius glued together, the answer is just 2.