Found problems: 13
The median, bisector, and height, all originate at the same vertex of a triangle. Given the intersection points of the median, bisector, and height with the circumscribed circle, construct the triangle.
Given points $M$ and $N$, the bases of heights $AM$ and $BN$ of $\vartriangle ABC$ and the line to which the side $AB$ belongs. Construct $\vartriangle ABC$.
Construct a triangle, the base of which lies on the given line, and the feet of the altitudes, drawn on the sides, coincide with the given points.
The center of the circle circumscribing $\vartriangle ABC$ is mirrored through each side of the triangle and three points are obtained: $O_1, O_2, O_3$. Reconstruct $\vartriangle ABC$ from $O_1, O_2, O_3$ if everything else is erased.
Construct a right-angled triangle along its two medians, starting from the acute angles.
Two points $K$ and $L$ are given on a circle. Construct a triangle $ABC$ so that its vertex $C$ and the intersection points of its medians $AK$ and $BL$ both lie on the circle, $K$ and $L$ being the midpoints of its sides $BC$ and $AC$.
The sides of the triangle $ABC$ lie on the sides of the angle $MAN$. Construct a triangle $ABC$ if the point $O$ of the intersection of its medians is given.
Construct a triangle given its height and median — both from the same vertex — and the radius of the circumscribed circle.
Given the base, height and the difference between the angles at the base of a triangle, construct the triangle.
Given three points $H_1, H_2, H_3$ on a plane. The points are the reflections of the intersection point of the heights of the triangle $\vartriangle ABC$ through its sides. Construct $\vartriangle ABC$.
Given two sides of the triangle. Construct that triangle, if medians to those sides are orthogonal.
Construct a right triangle, given two medians drawn to its legs.
All rectangles that can be inscribed in an isosceles triangle with two of their vertices on the triangle’s base have the same perimeter. Construct the triangle.