Geometry
Problems related to shapes, spaces, measurements, etc.
Problems in this category
Given a regular hexagon $ABCDEF$, $\vec{AB} = m$ and $\vec{BC} = n$. Express the vectors $\vec{BE}$,...
VectorsHexagonGeometric Vectors
2025/3/31
Given a regular hexagon $ABCDEF$, where $\vec{AB} = m$ and $\vec{BC} = n$, find the vectors $\vec{BE...
VectorsHexagonGeometric Proofs
2025/3/31
The sum of the number of diagonals and sides of a convex polygon is 55. Find the sum of the interior...
PolygonsDiagonalsInterior AnglesQuadratic Equations
2025/3/31
In a convex polygon, the sum of the number of diagonals and the number of sides is 55. What is the s...
PolygonsDiagonalsInterior AnglesQuadratic Equations
2025/3/31
A circle $k$ is circumscribed around triangle $ABC$. A tangent $t$ to the circle $k$ is constructed ...
GeometryCirclesCyclic QuadrilateralsTangent-Chord TheoremAnglesParallel LinesTriangleProof
2025/3/31
In an isosceles triangle, the bisector of a base angle intersects the opposite side (leg) at an angl...
TriangleIsosceles TriangleAngle BisectorAngle CalculationGeometric Proof
2025/3/31
We are asked to find the equations of lines given their distance from the origin, $p$, and the angle...
LinesCoordinate GeometryTrigonometryDistance from a Point to a LineEquation of a Line
2025/3/31
In triangle $ABC$, $BC > AC$. Point $D$ is on side $BC$ such that $BD = BC - AC$. Prove that line $A...
TriangleAngle BisectorIsosceles TriangleProofEuclidean Geometry
2025/3/31
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