Olympiad Corner: Which Number Is Erased?
Category: Olympiad Corner
Olympiad Corner: A Quadrilateral With Some Congruent Triangles
A quadrilateral ABCD is given. The midpoint of side AB is equidistant from three other sides of the quadrilateral. Prove that the square of AB…
Olympiad Corner: What Is The Sum Of The Corner Entries?
In a 4 x 4 array of 16 numbers, the sum of the numbers in each row, column, and diagonal is 1. Find the sum…
Olympiad Corner: Summing Up A Series
We have a series: tan(1)tan(2) + tan(2)tan(3) + … + tan(2019)tan(2020). What is its value? Here is a summation problem involving trigonometric functions. Do you…
Olympiad Corner: An Expression Under The Square Root
Find the product of four consecutive numbers. Add 1 to this product. Extract the square root of this expression. What is the value? How to…
Olympiad Corner: A Trig Touch To Geometry
AB is perpendicular to BC. E and F are two points on BC such that AB = BE = EF = FC. Angles AEB, AFB,…
Olympiad Corner: How Many Right Triangles?
How many right triangles have their area double of their perimeter? How to find the exact number of such triangles? Do you have a mathematical…
Olympiad Corner: Circle Inside, Circle Outside
A circle is inscribed in a triangle. And a circle is circumscribed about the same triangle. What is the ratio of their radii? Note that:…
Olympiad Corner: AM GM Inequality
Arithmetic mean is greater than or equal to Geometric mean. That is called AM – GM inequality. Here is a nice problem to show how…
Olympiad Corner: A Triangle Inside A Square
An equilateral triangle is drawn inside a unit square. How can we find its area? Do you have a mathematical question to ask? Do you…