Geometry
Problems related to shapes, spaces, measurements, etc.
Problems in this category
We are given a line segment $XY$ with coordinates $X(-8, -12)$ and $Y(p, q)$. The midpoint of $XY$ i...
Midpoint FormulaCoordinate GeometryLine Segment
2025/4/11
In the circle $ABCDE$, $EC$ is a diameter. Given that $\angle ABC = 158^{\circ}$, find $\angle ADE$.
CirclesCyclic QuadrilateralsInscribed AnglesAngles in a Circle
2025/4/11
Given the equation of an ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$, where $a \neq b$, we need ...
EllipseTangentsLocusCoordinate Geometry
2025/4/11
We are given a cone with base radius $r = 8$ cm and height $h = 11$ cm. We need to calculate the cur...
ConeSurface AreaPythagorean TheoremThree-dimensional Geometry
2025/4/11
$PQRS$ is a cyclic quadrilateral. We are given the measures of its angles in terms of $x$ and $y$. W...
Cyclic QuadrilateralAnglesLinear EquationsSolving Equations
2025/4/11
In the given diagram, line segment $MP$ is a tangent to circle $NQR$ at point $N$. $\angle PNQ = 64^...
Circle GeometryTangentsAnglesTrianglesIsosceles TriangleAlternate Segment Theorem
2025/4/11
We are given a diagram with two parallel lines intersected by two transversals. We need to find the ...
Parallel LinesTransversalsAnglesSupplementary Angles
2025/4/11
A trapezium with sides 10 cm and 21 cm, and height 8 cm is inscribed in a circle of radius 7 cm. The...
AreaTrapeziumCircleArea Calculation
2025/4/11
In circle $PQRS$ with center $O$, $\angle PQR = 72^\circ$ and $OR \parallel PS$. We need to find the...
Circle GeometryAnglesParallel LinesIsosceles Triangle
2025/4/11
The problem asks which of the given angles (66°, 72°, 24°, 15°) is not an exterior angle of a regula...
Regular PolygonExterior AnglePolygon Angle SumDivisibility
2025/4/11