Geometry
Problems related to shapes, spaces, measurements, etc.
Problems in this category
Point $D$ lies on side $BC$ of triangle $ABC$. $DC = 2BD$. Given that $\angle ABC = 45^{\circ}$ and ...
TriangleAnglesLaw of SinesTrigonometry
2025/3/31
Two circles $k_1$ and $k_2$ intersect at points $A$ and $B$. An arbitrary secant through $A$ interse...
CirclesCyclic QuadrilateralsParallel LinesAnglesSecantsIntersecting Circles
2025/3/31
Given a tangential quadrilateral $ABCD$, and $O$ is the center of the inscribed circle, prove that $...
GeometryTangential QuadrilateralInscribed CircleAnglesProof
2025/3/31
Let $M$, $N$, and $P$ be the points where the angle bisectors of the interior angles $\alpha$, $\bet...
GeometryTriangleCircumcircleAngle BisectorPerpendicular BisectorInscribed Angles
2025/3/31
The problem asks us to find the equations of lines given certain conditions. First, we need to find...
LinesEquation of a LineTrigonometryNormal Form of a Line
2025/3/31
Given a parallelogram $ABCD$. Point $E$ is on the line $BC$ such that $B$ is the midpoint of the seg...
VectorsParallelogramVector AdditionVector SubtractionMidpoint
2025/3/31
Given three vectors $\vec{u} = i + 2j - k$, $\vec{v} = 2i - j + 2k$, and $\vec{w} = 3i - 4j - 5k$. (...
VectorsDot ProductCross ProductOrthogonalityUnit Vector
2025/3/31
The problem asks us to find the intersections of the given lines with the Cartesian axes (x-axis and...
Linear EquationsCoordinate GeometryLinesIntersectionsx-axisy-axis
2025/3/31
We are asked to find the sum of the interior angles of the polygon shown in the image.
PolygonsInterior AnglesGeometric Formulas
2025/3/30
Given a regular hexagon $ABCDEF$, where $\vec{AB} = p$ and $\vec{BC} = q$, find the vectors $\vec{CD...
VectorsHexagonVector AdditionGeometric Proofs
2025/3/30