最新の問題
The problem has two parts. a) Prove that $\Omega$ belongs to the line (OG) and that it is the midpoi...
Euclidean GeometryTriangle GeometryEuler CircleCircumcircleCentroidOrthocenterEuler LineVector Geometry
2025/3/23
We are given a triangle $ABC$. $O$ is the circumcenter, $G$ is the centroid, and $H$ is the orthocen...
Triangle GeometryCircumcenterCentroidOrthocenterHomothetyEuler LineMedial TriangleVector Geometry
2025/3/23
Given three non-collinear points $A$, $B$, and $C$. For any point $M$ in the plane, we associate a p...
VectorsTransformationsHomothetyGeometric Transformations
2025/3/23
Given triangle $AIJ$ inscribed in circle $(C)$ with center $O$. Points $B$ and $C$ are symmetric to ...
HomothetyCirclesTrianglesCollinearityGeometric Transformations
2025/3/23
A line passing through a point M on segment $AB$ intersects segment $AC$ at point N. a) How should M...
TrianglesPerimeterAreaSimilarityProportionality
2025/3/23
The problem is based on an equilateral triangle $ABC$ with side length 4cm and center $O$. $\Gamma$ ...
VectorsEquilateral TriangleCircumcircleHomothetyGeometric Transformations
2025/3/23
放物線 $y = -2x^2$ を平行移動した放物線を $C$ とする。$C$ の頂点は直線 $y = 2x - 3$ 上にあり、$C$ は点 $(1, -5)$ を通っている。このとき、$C$ の方...
放物線平行移動二次関数方程式
2025/3/23
Given a triangle ABC, I is the midpoint of [AC]. $f_m$ is a transformation such that for any point M...
VectorsTransformationsTranslationsHomothetyChasles' Relation
2025/3/23
与えられた連立一次方程式を解く問題です。 $ \begin{cases} -10x - y = -6 \\ -9x - y = -5 \end{cases} $
連立一次方程式代入法方程式
2025/3/23
Given a line $(D)$, a point $A$ on $(D)$, and a point $B$ on the line perpendicular to $(D)$ that pa...
HomothetyGeometric TransformationsLocus of PointsVectorsParallel Lines
2025/3/23