Geometry
Problems related to shapes, spaces, measurements, etc.
Problems in this category
The problem asks us to find the coordinates of the focus and the equation of the directrix for each ...
Conic SectionsParabolasFocusDirectrixAnalytic Geometry
2025/5/30
Let $ABC$ be any triangle and let $P$ be any point of the segment $AB$. The parallel to the line $BC...
Triangle GeometryParallel LinesMidpoint TheoremSimilar TrianglesThales' Theorem
2025/5/29
In triangle $ABC$, points $E$ and $P$ lie on $AB$ such that $AE = EP = PB$. Points $F$ and $Q$ lie o...
Triangle SimilarityParallel LinesRatio and Proportion
2025/5/29
In triangle $ABC$, points $E$ and $P$ are on side $AB$ such that $AE = EP = PB$. Points $F$ and $Q$ ...
TriangleParallel LinesTriangle SimilarityThales' TheoremProportionality
2025/5/29
The problem provides a triangle $ABC$, a point $P$ on segment $[AB]$, and a line through $P$ paralle...
GeometryVectorsParallel LinesTriangleMidpoint
2025/5/29
The image presents a set of problems. We need to solve problem 4, which involves vector calculations...
VectorsCross ProductDot ProductVector AdditionVector Magnitude
2025/5/29
The problem is divided into two independent parts. Part I deals with a cube ABCDEFGH, with points I,...
VectorsPlanesLines3D GeometryDistance CalculationRotationsSimilarities
2025/5/27
A cable is tied from point G to point K on a sign FH. Point K is halfway up the sign FH. The distanc...
TrigonometryAnglesRight TrianglesTangentGeometric Proof
2025/5/27
The problem describes a fish shop with a vertical sign [FH] of height 3m. A cable is tied from the t...
Pythagorean TheoremTrigonometryRight TrianglesAngle CalculationTangent Function
2025/5/27
The problem asks to show that the size of the angle $FGH$ is $65^\circ$, correct to the nearest degr...
AnglesTrianglesCosine RuleGeometric Proofs
2025/5/27