### Building Tetrahedra

Can you make a tetrahedron whose faces all have the same perimeter?

### Ladder and Cube

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?

### Areas and Ratios

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 out.

# Incentre Angle

##### Stage: 4 Short Challenge Level:
See all short problems arranged by curriculum topic in the short problems collection

The three angle bisectors of triangle $LMN$ meet at a point $O$ as shown.

$\angle LNM$ is $68^{\circ}$. What is the size of $\angle LOM$?

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.