Geometry
Problems related to shapes, spaces, measurements, etc.
Problems in this category
The problem asks to find the tangent of the two acute angles, $M$ and $N$, in a given right triangle...
TrigonometryRight TrianglesTangentRatios
2025/4/14
The problem is to find the standard form of the equation of a circle given its general form: $x^2 + ...
CirclesEquation of a CircleCompleting the Square
2025/4/14
The problem is to identify the type of quadric surface represented by the equation $9x^2 + 25y^2 + 9...
Quadric SurfacesEllipsoids3D GeometryEquation of a Surface
2025/4/14
The problem asks us to analyze the equation $x^2 + y^2 - 8x + 4y + 13 = 0$. We need to determine wh...
CirclesCompleting the SquareEquation of a CircleCoordinate Geometry
2025/4/14
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