Select Page

Understand the problem

Cauchy Schwarz Inequality is a powerful tool in Algebra. It was beautiful geometric implications as well. Watch the video and solve the tutorial problems to delve deep into the idea.

Tutorial Problems!

1. Look at the expression $$\sqrt{x_1^2 + y_1^2} \times \sqrt {x_2^2 + y_2^2} \geq (x_1 x_2 + y_1 y_2 )$$

Can you simply square both sides and prove this ?

2. Show that if A, B are any two points in the plane and O is the origin then cosine of the angle AOB is the ratio of $$\frac{\text{dot product of the coordinates}} {\text{product of their distances from origin}}$$

Connected Program at Cheenta

Math Olympiad is the greatest and most challenging academic contest for school students. Brilliant school students from over 100 countries participate in it every year.

Cheenta works with small groups of gifted students through an intense training program. It is a deeply personalized journey toward intellectual prowess and technical sophistication.

Similar Problems

A trigonometric polynomial ( INMO 2020 Problem 2)

Indian National Math Olympiad (INMO 2020) Solution and sequential hints to problem 2

Kites in Geometry | INMO 2020 Problem 1

Try this beautiful geometry problem from INMO (Indian National Math Olympiad) 2020). We provide solution with sequential hints so that you can try.

Geometry of AM GM Inequality

AM GM Inequality has a geometric interpretation. Watch the video discussion on it and try some hint problems to sharpen your skills.

Geometry of Cauchy Schwarz Inequality

Cauchy Schwarz Inequality is a powerful tool in Algebra. However it also has a geometric meaning. We provide video and problem sequence to explore that.

RMO 2019 Maharashtra and Goa Problem 2 Geometry

Understand the problemGiven a circle $latex \Gamma$, let $latex P$ be a point in its interior, and let $latex l$ be a line passing through $latex P$.  Construct with proof using a ruler and compass, all circles which pass through $latex P$, are tangent to \$latex...

RMO 2019 (Maharashtra Goa) Adding GCDs

Can you add GCDs? This problem from RMO 2019 (Maharashtra region) has a beautiful solution. We also give some bonus questions for you to try.

Number Theory, Ireland MO 2018, Problem 9

This problem in number theory is an elegant applications of the ideas of quadratic and cubic residues of a number. Try with our sequential hints.

Number Theory, France IMO TST 2012, Problem 3

This problem is an advanced number theory problem using the ideas of lifting the exponents. Try with our sequential hints.

Algebra, Austria MO 2016, Problem 4

This algebra problem is an elegant application of culminating the ideas of polynomials to give a simple proof of an inequality. Try with our sequential hints.

Number Theory, Cyprus IMO TST 2018, Problem 1

This problem is a beautiful and simple application of the ideas of inequality and bounds in number theory. Try with our sequential hints.