Understanding Simson Lines

Understanding Simson Lines

Imagine a point P floating in the plane of a triangle ABC. How far is this point from the sides of the triangle? A point P is floating in the plane of a triangle ABC Think: Suppose ABC is a triangle. Specify three positive numbers: x, y, z (for example 2, 3, 4.9). Is...
What if a Simson Line moves!

What if a Simson Line moves!

This is the story of a deltoid. It is known as Steiner Hypocycloid. It looks like a curved sided triangle. And it is traced out by something called a Simson line. Let us start the story from the beginning. We have a triangle ABC. We draw its circumcircle. And we pick...
A Dream, An IMO 2018 Problem and A Why

A Dream, An IMO 2018 Problem and A Why

Cheenta, with the zeal of a child, has a dream of training a perfect IMO team someday in the recent future. Also, the day, 22nd December is very special to Mathematics, which saw the birth of Ramanujan and is a very romantic day for every math-loving person. With that...
2016 ISI Objective Solution Problem 1

2016 ISI Objective Solution Problem 1

Problem The polynomial \(x^7+x^2+1\) is divisible by (A) \(x^5-x^4+x^2-x+1\) (B) \(x^5-x^4+x^2+1\) (C) \(x^5+x^4+x^2+x+1\) (D) \(x^5-x^4+x^2+x+1\) . Also Visit: I.S.I. & C.M.I Entrance Program Understanding the Problem: The problem is easy...