Kite in a Circle – Pre RMO 2017, Problem 13

Kite in a Circle – Pre RMO 2017, Problem 13

Cyclic Quadrilaterals are often important objects in a Geometry problem. Recognizing them can lead to a path to the solution. A case in point is this problem from Pre RMO 2017. How to recognize cyclic quadrilaterals?  Opposite angles add up to \( \pi \) Two angles...
PreRMO and I.S.I. Entrance Open Seminar

PreRMO and I.S.I. Entrance Open Seminar

Advanced Mathematics Seminar  2 hours An Open seminar for Pre-RMO and I.S.I. Entrance 2019 aspirants.  We will work on topics from Number Theory, Geometry and Algebra.  Registration is free. There are only 25 seats available. Date: 29th June, Friday, 6 PM Online...
Geometry of Algebra

Geometry of Algebra

It is interesting to represent Algebraic Identities using Geometric objects. One easy example is presented in this video. Think! Try to draw the following algebraic identities using geometric objects \(a^2 – b^2 = (a+b)(a-b) \) \( (a+b)^3 = a^3 + 3a^2 b + 3 ab^2...
Injection Principle – Combinatorics

Injection Principle – Combinatorics

The central goal of Combinatorics is to count things. Usually, there is a set of stuff that you would want to count. It could be number of permutations, number of seating arrangements, number of primes from 1 to 1 million and so on. Counting number of elements in a...
Orthocenter and equal circles

Orthocenter and equal circles

Orthocenter (or the intersection point of altitudes) has an interesting construction. Take three equal circles, and make them pass through one point H. Their other point of intersection creates a triangle ABC. Turns out, H is the orthocenter of ABC. In this process,...