For questions about geometric shapes, congruences, similarities, transformations, as well as the properties of classes of figures, points, lines, angles.

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3
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1answer
127 views
+50

Square-To what should $x$ be equal?

At the side $AD=a$ of the square $ABCD$, we take the point $E$ and at the extension of $AB$ the point $Z$, such that $DE=BZ=x$. a) Show that the line bisector of $EZ$ goes through the vertex $C$. ...
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vote
0answers
382 views
+100

Fitting Expanding Spheres in the Irregular Surface

This is a kind of a puzzle: I have a convex hull filled with $N$ small spheres(with radius $r$). Now, the balls grow in size till it hit any side of the Cavity (Convex hull) or any other ball. ...
3
votes
1answer
47 views
+50

An equilateral triangle formed using points of tangency

P.S:I am looking for a hint and not the whole solution. BdMO 2012 nationals secondary: The vertices of a right triangle $ABC$ inscribed in a circle divide the circumference into three arcs. The ...