The six intersection points of a triangle’s non-parallel altitudes and perpendicular bisectors are the vertices of two congruent minor periambic triangles which are inversely similar to the original.

Now use the information you already have about finding the equation of a line and apply it to the dashed lines shown in these triangles. Remember, to find the equation of a line you need a point ...

In the diagram below, AB is the chord of a circle with centre O. OM is perpendicular to AB (meet at a right angle). Look at triangles OAM and OBM. The hypotenuses (OA and OB) are the same, as they are ...

The Monthly publishes articles, as well as notes and other features, about mathematics and the profession. Its readers span a broad spectrum of mathematical interests, and include professional ...