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...
Leibniz Rule, ISI 2018 Problem 4

Leibniz Rule, ISI 2018 Problem 4

The Problem Let \(f:(0,\infty)\to\mathbb{R}\) be a continuous function such that for all \(x\in(0,\infty)\), $$f(2x)=f(x)$$Show that the function \(g\) defined by the equation $$g(x)=\int_{x}^{2x} f(t)\frac{dt}{t}~~\text{for}~x>0$$is a constant function. Key Ideas One...