Circle in Circle – PRMO 2017

Circle in Circle – PRMO 2017

Understand the problem Let ( Omega_1 ) be a circle with center O and let AB be a diameter of ( Omega_1 ). Let P be a point on the segment OB different from O. Suppose another circle ( Omega_2 ) with center P lies in the interior of ( Omega_1 ). Tangents are drawn from...
What is the boundary?

What is the boundary?

Boundaries are controversial. Ask the politicians! Mathematicians, on the other hand, have an interesting way of thinking about the boundary of the space. It is less controversial for sure. Pick any point in the space. Draw rays emanating from that point. How do you...
Locus of vertex of an equilateral triangle

Locus of vertex of an equilateral triangle

Try this beautiful problem. We will give you hints! ABC is an equilateral triangle with vertex A fixed and B moving in a given straight line. Find the locus of C   What is the big idea ? Think about what does not change. 1. Point A is fixed. 2. The line on which...

Group Theory open seminar

Group Theory Open seminar April 20, Saturday, 6 PM I.S.T. ; Abstract A great way to study groups is to study group automorphisms. They are structure-preserving maps from a group to itself. Some subgroups are ‘invariant’ under all group automorphisms. They...
Pappus Theorem – Story from Math Olympiad

Pappus Theorem – Story from Math Olympiad

Alexander the great founded Alexandria in Egypt. This was in the year 332 Before Christ.  Since then Alexandria became one of the most important cities of the world. It had the Light House and the Great Library. These were the wonders of ancient world. ...