Tag Archives: AoPS

Total number of integer ordered pairs that satisfy the difference between Arithmetic mean and Geometric mean is 1

Posted on June 25, 2024 by Sumant Sumant

Suppose (a,b) are non negative integers such that and . Find the number of ordered pairs that satisfy the above condition. (Australian Mathematical Olympiad, 2020)

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Coloring a 3 by 3 grid using two colors ( blue and orange) so that no row or column contains more than one orange color

Posted on June 23, 2024 by Sumant Sumant

Sumant colors each square in an empty 3 by 3 grid either blue or orange. Find the total number of ways to color the grid so that no toes or columns contain more than one orange.

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Spotting difference in squares

Posted on June 15, 2024 by Sumant Sumant

Simplify

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a simple median on Right Triangle proof

Posted on June 12, 2024 by Sumant Sumant
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An easy question for teaching exponents

Posted on June 2, 2024 by Sumant Sumant

Given and . Determine the possible values of $x^2y2z^2$

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Fixed piece of wire bent into square and rectangle. For minimum total area what should be the perimeter of each.

Posted on June 2, 2024 by Sumant Sumant

A 30 cm piece of wire is cut into two. One piece is bent into the shape of a square, the other piece into the share of a rectangle with a length to width ratio of 2:1. What are the … Continue reading →

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Two parabolas passing through their corresponding vertices

Posted on June 2, 2024 by Sumant Sumant

The parabola has vertex and the parabola has vertex where and are distinct points. The two parabolas intersect at and . Prove that .

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Find max area of inscribed rectangle in an isosceles triangle

Posted on June 2, 2024 by Sumant Sumant

An isosceles triangle has a base of 6m and height 4m. Find a rectangle of max area inscribed in that triangle.

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Angle subtended at mid point is 1/2 of angle subtended at 3/4 in a square from the same vertex

Posted on May 29, 2024 by Sumant Sumant

In a square ABCD, M is the midpoint of AD and N is the midpoint of MD. Prove that . See alsohttps://sumantmath.wordpress.com/2024/05/29/a-geometry-problem-solved-using-trigonometry/

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A Geometry problem solved using Trigonometry

Posted on May 29, 2024 by Sumant Sumant

In a square ABCD, M is the midpoint of AD and N is the midpoint of MD. Prove that .

Posted in Geometry | Tagged , , | 2 Comments