Geometry
Problems related to shapes, spaces, measurements, etc.
Problems in this category
The problem asks us to find four inequalities that define the unshaded region R in the given XOY pla...
Linear InequalitiesCoordinate GeometryRegions in the PlaneLines
2025/3/27
The problem asks to convert the polar equation $r = \frac{4}{1 + 2\sin\theta}$ to a rectangular equa...
Polar CoordinatesRectangular CoordinatesCoordinate ConversionConic SectionsHyperbola
2025/3/27
The problem is to convert the polar equation $r = \frac{-4}{\cos \theta}$ to rectangular coordinates...
Polar CoordinatesRectangular CoordinatesCoordinate Transformation
2025/3/27
Given points $A(-1, -3)$ and $B(0, -1)$, and vector $\vec{a} = (2, y)$. Also, $\vec{AB} // \vec{a}$....
VectorsCoordinate GeometryParallel Vectors
2025/3/27
Given two vectors $a = (1, -1)$ and $b = (m+1, 2m-4)$, if $a$ is perpendicular to $b$, find the valu...
VectorsDot ProductPerpendicular Vectors
2025/3/27
We are given an isosceles right triangle $ABC$. On its sides, isosceles right triangles $BCO_1$, $AC...
VectorsGeometry of TrianglesIsosceles Right TrianglesVector AdditionGeometric Transformations
2025/3/27
Given a triangle $ABC$ where $\vec{AC} = \vec{a}$ and $\vec{BC} = \vec{b}$. A square $ACDE$ is const...
VectorsGeometry of SquaresVector AdditionGeometric Proof
2025/3/27
Given a triangle with side lengths $a$, $b$, and $c$, and the length of the median to side $a$ denot...
Triangle InequalityMedianApollonius's TheoremGeometric Inequalities
2025/3/27
We are given a regular hexagon $ABCDEF$. We are given that the vector $\vec{AB} = p$ and the vector ...
VectorsGeometryHexagonVector Addition
2025/3/27
Given a regular hexagon $ABCDEF$, and $\vec{AB} = p$ and $\vec{BC} = q$, we need to find the vectors...
VectorsGeometryHexagonVector AdditionVector Subtraction
2025/3/27