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Today we shall have a look at a simple configuration which is moderately prevalent in modern Olympiads but has not received much attention. Our work shall involve the feet of the perpendiculars from the foot of the $latex A-$altitude to the sides $latex AB$ and $latex AC$. As usual, notation is borrowed from the diagram… Continue reading Feet to the sides from the A-foot
This blog post corresponds to my newest olympiad handout on discrete continuity. The concept of discrete continuity is an extremely effective and versatile method in tackling a wide variety of combinatorics problems. This technique has been used extensively for many years especially in particular classes of problems. Here, after a quick recap of the basics we shall… Continue reading Discrete Continuity in Combinatorics
In this article, we shall explore some properties of the intersections two highly celebrated circles in the world of Olympiad geometry. Although the individual circles are thoroughly explored and considered mostly 'well-known', the configuration involving their intersections is still relatively unexplored, with only two notable examples appearing on an Olympiad to date, as far as… Continue reading Intersections of the Nine-Point Circle and (BHC)
In this article we provide investigate a famous classical process involving piles of stones (or originally cards) introduced by Martin Gardner. The game involves a set of piles of stones with $latex \frac{n(n+1)}{2}$ stones in total. In each move, the topmost stone in each pile is picked and a new pile is formed with these… Continue reading Bulgarian Solitaire
Today we will revisit a rather old but underrated configuration which has certain beautiful properties. Our work shall revolve around the points $latex E$ on $latex AC$ and $latex F$ on $latex AB$ such that $latex AE=AF$ and points $latex E,H$ and $latex F$ lie on a straight line.Shoutouts to raosicheng for suggesting an overwhleming… Continue reading Isosceles triangle with the orthocenter on the base
Today we will explore the properties of a certain well-known point with respect to the intouch triangle. The Why Point, originally seen in the famous 2011 G4, is a thoroughly explored configuration with a plethora of interesting properties. Among the many perspectives of the Why Point configuration is the Why Point of the Intouch triangle.Here… Continue reading Why Point of the Intouch Triangle
This article will explore a relatively new configuration which I have talked about extensively in my handout Neat Config which was crafted from a series of notes made by Om Kutte for lectures conducted by him at the (Unofficial) Indian National Mathematical Olympiad Training Camp. This is the master diagram. All the point definitions (and… Continue reading Miquel Point of the Angle Bisectors
In this post we will have a look at three really common triangle length conditions. They look almost the same but their slightly different definitions invoke highly contrasting configurations. After introducing each condition, and looking at how it can be interpreted, we solve (at least partially) some contest problems involving those conditions. 1. Equal Lengths… Continue reading Some Length Conditions on a Triangle
Angular Momentum 