Here is a result I worked out using the theorems of Ceva and Menelaus.

**The points P, Q and R lie on the sides BC, CA and AB of triangle ABC respectively (not necessarily in their interiors), such that they are not collinear.** 263 more words

## Tags » If And Only If

#### Ceva and Menelaus

#### 60 degrees special property

The triangle ABC has circumcentre O, incentre I and orthocentre H.

**A, O, I, H and C are concyclic if and only if ∠ABC = 60°.** 338 more words

#### More cyclic quadrilaterals

Just to pass the time, a very simple result (again found by playing on Geogebra):

A triangle ABC is acute-angled. The point P is located in the interior of ABC. 286 more words

#### Propositional Logic: Building Propositions

Previously, we focused on basic propositions and how they play a part in arguments. But in addition to the rather straightforward types of propositions we saw, we can also use… 754 more words

#### Three circles and one egg

**Two circles, X and Y, intersect at two points A and B. One line is drawn through X, cutting it at two points, P and Q; another line, not parallel to the first, is drawn through Y, cutting it at two points, R and S.** 350 more words

#### "Nervosa" in If and Only If, Issue Two!

As I mentioned a couple posts ago, I had a short poem published in the new issue of *If and Only If: A Journal of Body Image and Eating Disorders…* 15 more words