Geometry

Problems related to shapes, spaces, measurements, etc.

Problems in this category

Given a tangential quadrilateral $ABCD$, and $O$ is the center of the inscribed circle, prove that $...

GeometryTangential QuadrilateralInscribed CircleAnglesProof

Let $M$, $N$, and $P$ be the points where the angle bisectors of the interior angles $\alpha$, $\bet...

GeometryTriangleCircumcircleAngle BisectorPerpendicular BisectorInscribed Angles

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

Given a parallelogram $ABCD$. Point $E$ is on the line $BC$ such that $B$ is the midpoint of the seg...

VectorsParallelogramVector AdditionVector SubtractionMidpoint

Given three vectors $\vec{u} = i + 2j - k$, $\vec{v} = 2i - j + 2k$, and $\vec{w} = 3i - 4j - 5k$. (...

VectorsDot ProductCross ProductOrthogonalityUnit Vector

The problem asks us to find the intersections of the given lines with the Cartesian axes (x-axis and...

Linear EquationsCoordinate GeometryLinesIntersectionsx-axisy-axis

We are asked to find the sum of the interior angles of the polygon shown in the image.

PolygonsInterior AnglesGeometric Formulas

Given a regular hexagon $ABCDEF$, where $\vec{AB} = p$ and $\vec{BC} = q$, find the vectors $\vec{CD...

VectorsHexagonVector AdditionGeometric Proofs

Given a regular hexagon $ABCDEF$, where $\vec{AB} = \vec{p}$ and $\vec{BC} = \vec{q}$, express the v...

VectorsHexagonGeometric Transformations

We are given a regular hexagon $ABCDEF$. We are given that $\vec{AB} = p$ and $\vec{BC} = q$. We nee...

VectorsHexagonVector AdditionGeometric Transformations

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