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Monthly Archives: December 2025
Square root extractor
How could you quickly find the square root of any number without log table or slide rule or any mathematical calculation, infact with nothing on hand but a pair of compasses and a graduated rule?
The Plate of Pie
Diameter of the smallest circular plate on which a semi-circular pie can be placed if the pie is cut in sectors of the same radius as the pie.
Pascal Contest 2023 Question 20 on Circles
Four larger circles with radius 5 are arranged so that the centers are the vertices of a square. Each of the larger circles is tangent to (that is, just touches) two of the other circles as shown. A smaller circle … Continue reading
2023 Cayley Contest Question 23 on Quarter Circle
In the diagram ABC is a quarter circle centered at B. Each of the squares PQRS, square SRTB and square RUVT has side length 10. Points P and S are on AB, points T and V are on BC and … Continue reading
2024 Pascal Contest Question 24 on Quarter Circles
2024 Pascal contest question 24. The key insight is to label the disjoint regions. Continue reading
Equilateral triangles on adjacent sides of a random Parallelogram
Prove that a triangle drawn by connecting the vertices of two equilateral triangles drawn on the adjacent side of a random parallelogram is an equilateral triangle
Equilateral triangles on the sides of a random triangle
Explore the problem using Geogebra Given a random triangle ABC. Draw two equilateral sides on sides AB and AC facing outwards. Let these equilateral triangles be ABD and ACE. Prove that DC = BE.
Sumant's 1 page of Math 