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