Can you make a tetrahedron whose faces all have the same perimeter?
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?
What is the area of the quadrilateral APOQ? Working on the building
blocks will give you some insights that may help you to work it
Three circles $C_1$, $C_2$ and $C_3$, of radii 1 cm, 2 cm and 3 cm respectively touch as shown. $C_1$ meets $C_2$ at $P$ and meets $C_3$ at $Q$.
What is the length in cm of the longer arc of circle $C_1$ between $P$ and $Q$?
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.
This problem is taken from the UKMT Mathematical Challenges.