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

1974 Chisinau City MO, 75
Tags: line construction , equal area , geometry
Through point $P$, which lies on one of the sides of the triangle $ABC$, draw a line dividing its area in half.

1939 Moscow Mathematical Olympiad, 045
Tags: sum , geometric construction , line construction , geometry
Consider points $A, B, C$. Draw a line through $A$ so that the sum of distances from $B$ and $C$ to this line is equal to the length of a given segment.

1936 Moscow Mathematical Olympiad, 028
Tags: geometry , geometric construction , line construction , perimeter
Given an angle less than $180^o$, and a point $M$ outside the angle. Draw a line through $M$ so that the triangle, whose vertices are the vertex of the angle and the intersection points of its legs with the line drawn, has a given perimeter.

1997 Tournament Of Towns, (552) 2
Tags: geometric construction , line construction , geometry
$M$ is the midpoint of the side $BC$ of a triangle $ABC$. Construct a line $\ell$ intersecting the triangle and parallel to $BC$ such that the segment of $\ell$ between the sides $AB$ and $AC$ is the hypotenuse of a right-angled triangle with $M$ being its third vertex. (Folklore)

1987 Tournament Of Towns, (153) 4
Tags: geometry , bisects area , line construction , arc , broken line , line
We are given a figure bounded by arc $AC$ of a circle, and a broken line $ABC$, with the arc and broken line being on opposite sides of the chord $AC$. Construct a line passing through the mid-point of arc $AC$ and dividing the area of the figure into two regions of equal area.