Geometry

Problems related to shapes, spaces, measurements, etc.

Problems in this category

Two ladders, $PS$ and $QT$, are placed against a vertical wall $TR$. $PS = 10$ m and $QT = 12$ m. Th...

TrigonometryRight TrianglesAnglesCosineSineWord Problem
2025/4/13

In the given diagram, $TB$ is a tangent to the circle at point $B$, and $BD$ is the diameter of the ...

Circle TheoremsAngles in a CircleCyclic QuadrilateralsTangentsDiameter
2025/4/13

Araba walked $2t$ km from village S to village T on a bearing of $065^\circ$. Then, she walked $3t$ ...

TrigonometryBearingPythagorean TheoremAngles
2025/4/13

In circle $PQRST$ with center $O$, $POR$ and $QOT$ are straight lines. $QT$ is parallel to $RS$. Ang...

CirclesAnglesTrianglesIsosceles TrianglesParallel Lines
2025/4/13

We are given a triangle $ABC$ with an altitude $BD$. We know that $|AB|=13$, $|BD|=12$, and $|DC|=4$...

TrianglesPythagorean TheoremAltitudeRight Triangles
2025/4/13

The problem asks to find the symmetric equations of the tangent line to the curve given by the vecto...

Vector CalculusTangent LinesParametric EquationsSymmetric Equations3D Geometry
2025/4/13

The problem asks us to find the equation of a plane that contains two given parallel lines. The para...

Plane GeometryVectorsCross ProductParametric EquationsLines in 3DEquation of a Plane
2025/4/13

The problem asks to find the symmetric equations of the line of intersection of two given planes. Th...

LinesPlanesVector AlgebraCross ProductLinear Equations
2025/4/13

The problem requires us to write an algorithm (in pseudocode) that calculates the area of a circle. ...

AreaCircleAlgorithmPseudocode
2025/4/13

The problem asks us to find the parametric and symmetric equations of a line that passes through a g...

Lines in 3DParametric EquationsSymmetric EquationsVectors
2025/4/13