This website contains problems from math contests. Problems and corresponding tags were obtained from the Art of Problem Solving website.

Tags were heavily modified to better represent problems.

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Found problems: 5

Ukraine Correspondence MO - geometry, 2009.3
A right triangle is drawn on the plane. How to use only a compass to mark two points, such that the distance between them is equal to the diameter of the circle inscribed in this triangle?
right triangle inradius geometry compass right triangles

2022 Moscow Mathematical Olympiad, 2
In a Cartesian coordinate system (with the same scale on the x and y axes)there is a graph of the exponential function $y=3^x$. Then the y-axis and all marks on the x-axis erased. Only the graph of the function and the x-axis remained without a scale and a mark of $0$. How can you restore the y-axis using a compass and ruler?
ruler geometry compass analytic geometry algebra combinatorics

1996 Tuymaada Olympiad, 4
Given a segment of length $7\sqrt3$ . Is it possible to use only compass to construct a segment of length $\sqrt7$?
construction geometry compass geometric constructions

2021/2022 Tournament of Towns, P2
On a blank paper there were drawn two perpendicular axes $x$ and $y$ with the same scale. The graph of a function $y=f(x)$ was drawn in this coordinate system. Then the $y$ axis and all the scale marks on the $x$ axis were erased. Provide a way how to draw again the $y$ axis using pencil, ruler and compass: (a) $f(x)= 3^x$; (b) $f(x)= \log_a x$, where $a>1$ is an unknown number.
function ruler geometry compass analytic geometry algebra combinatorics

2013 Oral Moscow Geometry Olympiad, 2
With a compass and a ruler, split a triangle into two smaller triangles with the same sum of squares of sides.
ruler construction geometry compass geometric constructions