Geometry
Problems related to shapes, spaces, measurements, etc.
Problems in this category
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
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
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
Given a triangle ABC with a right angle at B, where $AC = 12$ cm and $\angle ACB = 145^\circ$. We ne...
TrigonometryTrianglesRight TrianglesSineCosineTangent
2025/3/23
Find the equation of the line passing through the point $(4, 5)$ and parallel to the line $y = x - 1...
Linear EquationsParallel LinesCoordinate GeometrySlope-intercept form
2025/3/22
The problem asks for the equation of a vertical line that passes through the point $(-1, -2)$.
Coordinate GeometryLinesVertical LinesEquations of Lines
2025/3/21