Inversion and Ptolemy’s Theorem

Inversion and Ptolemy’s Theorem

Understand the problem Ptolemy’s Theorem gives a relation between product of diagonals of a quadrilateral with the sum of the product of its opposite sides. However it can be proved using tools from inversive geometry (that Ptolemy probably did not know). Try...
Kites in Geometry | INMO 2020 Problem 1

Kites in Geometry | INMO 2020 Problem 1

Understand the problem Let ( Gamma_1 ) and ( Gamma_2 ) be two circles with unequal radii, with centers (  O_1 ) and ( O_2 ) respectively, in the plane intersecting in two distinct points A and B. Assume that the center of each of the circles ( Gamma_1 ) and ( Gamma_2...
Extremal Principle for Counting – AMC 10

Extremal Principle for Counting – AMC 10

Extremal Principle is used in a variety of problems in Math Olympiad. The following problem from AMC 10 is a very nice example of this idea. AMC 10 Problem 4 (2019)- Based on Extremal Principle A box contains 28 red balls, 20 green balls, 19 yellow balls, 13 blue...
Spiral Similarity

Spiral Similarity

Geometric Transformation is a powerful tool in Geometry. We look at one such transformation: Spiral Similarity. Watch video Try these Spiral Similarity problems. Send answers to helpdesk@cheenta.com Problem 1: Suppose O = (0, 0), A = (2, 0) and B = (0, 2). Let T be...
AMC 8 2019 – Stick and Dot Method

AMC 8 2019 – Stick and Dot Method

Understand the problem Alice has 24 apples. In how many ways can she share them with Becky and Chris so that each of the three people has at least two apples? Source of the problem American Mathematical Contest 2019, AMC 8 Problem 25 Topic Combinatorics  Difficulty...