An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
Rectangle PQRS has X and Y on the edges. Triangles PQY, YRX and XSP
have equal areas. Prove X and Y divide the sides of PQRS in the
A 1 metre cube has one face on the ground and one face against a
wall. A 4 metre ladder leans against the wall and just touches the
cube. How high is the top of the ladder above the ground?
Let AB have length 3r. The distance moved by A is then the
circumference of a semicircle radius 3r (3$\pi$r). C moves along a
circle of radius 2r (2$\pi$r), followed by a semicircle of radius r
($\pi$r). The total distance moved by C is therefore also 3$\pi$r.
This problem is taken from the UKMT Mathematical Challenges.