A quarter-circle with radius is drawn. Inside it, two semicircles and a circle are drawn as shown in the above figure. If the area of the grey colored region is find the value of
is inscribed in a circle such that . If and are adjacent vertices of a regular -gon inscribed in the circle, find .
Details and Assumptions
In a circle with center , a chord is drawn such that . Radius . A circle is drawn in the major arc such that it's radius is maximum, with center E, it touches the larger circle at point X as shown in figure.
The area of the shaded region can be expressed as for integers with What is the value of ?
You are a farmer, with a round fenced field of radius meters. You tie your goat to the fence with a rope, and realize that the goat can eat exactly of the field. How long is the rope?
Note: You can use a computational solver for the last step of the problem.
Find the area of the blue shaded region in this rectangle, with two semicircles of radius 7 drawn.