RMO 2018 Tamil Nadu Problem 3 Sequential Hints and Solution. A number theory problem with a pinch from diophantine equation.
RMO 2018 Tamil Nadu Problem 3 Sequential Hints and Solution. A number theory problem with a pinch from diophantine equation.
RMO 2018 Tamil Nadu Problem 2 Sequential Hints and Solution. A polynomial problem with seasoning from geometric progression.
RMO 2018 Tamil Nadu Problem 1 Sequential Hints and Solution. A beautiful geometry problem that uses properties of cyclic quadrilaterals.
Regional Math Olympiad (Tamil Nadu Region, 2018) Problems, Sequential Hints and Discussion.
The golden ratio is arguably the third most interesting number in mathematics. We explore a beautiful problem connecting Number Theory and Geometry.
Parity and divisibility are two interesting tools of elementary number theory. Coupled with an estimation with AM-GM inequality, we have excursion into the queen of mathematical disciplines.
This post contains RMO 2018 solutions, problems, and discussions. RMO 2018, Problem 1: Let \(ABC\) be a triangle with integer sides in which \(AB < AC\). Let the tangent to the circumcircle of triangle \(ABC\) at \(A\) intersect the line \(BC\) at \(D\). Suppose \(AD\) is also an integer. Prove that gcd\((AB,AC) >1\). RMO 2018, […]
A convex polygon \( \Gamma \) is such that the distance between any two vertices of \( \Gamma \) does not exceed 1. Prove that the distance between any two points on the boundary of \( \Gamma \) does not exceed 1. If X and Y are two distinct points inside \( \Gamma \), prove that […]
The Problem Let ABC be a triangle in which AB = AC and let I be its in-centre. Suppose BC = AB + AI. Find ∠BAC. Big Ideas For any triangle ABC, \( \frac{\sin A}{a} = \frac{\sin B } {b} = \frac {\sin C }{c} \). Addendo: If \( \frac{a}{b} = \frac{c}{d} \) then each of […]
Recently, French mathematician Cedric Villani's team came up with '21 measures for the teaching of Mathematics'. I read through the report, with great curiosity. I happily noted that Cheenta's Thousand Flowers program has already implemented some of his recommendations.