Can you find a relationship between the area of the crescents and the area of the triangle?
Weekly Problem 5 - 2006
How many times does the inside disc have to roll around the inside of the ring to return to its initial position?
The diagram shows two semicircular arcs... What is the diameter of the shaded region?
The diagram shows two circles and four equal semi-circular arcs. The area of the inner shaded circle is 1. What is the area of the outer circle?
Three circles of different radii each touch the other two. What can you deduce about the arc length between these points?
The diagram shows a regular pentagon with sides of unit length. Find all the angles in the diagram. Prove that the quadrilateral shown in red is a rhombus.
Two circles of equal size intersect and the centre of each circle is on the circumference of the other. What is the area of the intersection? Now imagine that the diagram represents two spheres of equal volume with the centre of each sphere on the surface of the other. What is the volume of intersection?
This pattern of six circles contains three unit circles. Work out the radii of the other three circles and the relationship between them.
Three semi-circles have a common diameter, each touches the other two and two lie inside the biggest one. What is the radius of the circle that touches all three semi-circles?
