Interesting problem on area and triangle.

A question about angle bisectors Consider a △ABC in which D, E and F are the midpoints of the sides BC, CA and AB respectively. Let G be the centroid of triangle ABC, i.e., the point of intersection of the medians AD, BE and CF. It is well-known that G is also the centroid of triangle DEF. If, instead of being the midpoints, the points D, E and F are the points of intersection of the internal bisectors of

In an article published in the November 2016 issue of At Right Angles we had seen how geometrical fractal constructions lead to algebraic thinking. The article had highlighted the iterative construction processes, which lead to the Sierpinski triangle and the Sierpinski Square carpet. Further the idea of self-similarity within these fractals was reinforced through the recursive and explicit relationships between various stages of the fractal constructions.

On the Facebook page (AtRiUM: At Right Angles, Us and Math) linked to this magazine, one of our contributors, Arsalan Wares, has been astonishingly prolific in posting problems. A good many of these have had to do with regular hexagons; more specifically, with the areas of polygonal regions drawn within such hexagons. It is both astonishing and pleasing to see such a rich diversity of problems arising from this simple and familiar structure.

In this article, we focus on investigations with graph paper. Pages 45 & 46 give guidelines for the facilitator, pages 43 & 44 are a worksheet for students. This time we explore quadrilaterals and triangles using lattice points.

Here is an alternative solution to the following problem which was studied in the November 2016 issue of AtRiA:

Two sides of a triangle have lengths 6 and 10, and the radius of the circumcircle of the triangle is 12. Find the length of the third side.

Counting and the study of mathematics go a long way back. In this article, geometry and counting come together to provide an interesting window to mathematical thinking and reasoning. Geometrical constructions provide a hands-on aspect and teachers of classes 6-10 can use this article to design GeoGebra investigations, mathematical discussions with trigger questions or even an unusual revision worksheet.

LinkedIn reader Peter Lovasz asks: Among all triangles that share a given circle as incircle, which one has the smallest perimeter?

In this edition of ‘Adventures’ we study a few miscellaneous problems, some from past RMOs. As usual, we pose the problems first and give the solutions later in the article, thereby giving you an opportunity to work on the problems.

In this short note we start with a simple problem concerning a triangle and then analyze new problems derived from it by changing the hypothesis.


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