Summary We prove the next generalization of the Steiner-Lehmus theorem: if two equal cevians intersect with each other on the angle bisector of the third triangle vertex, then the triangle is ...

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.

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 secret to getting ahead is getting started. In the triangle above, segment BD is an angle bisector. Sides AB = 9x − 14, BC = 4x − 3, CD = 2x + 11 and AD = 5x + 2. Find the area of triangle ABD and ...