Geometry
Problems related to shapes, spaces, measurements, etc.
Problems in this category
The diagram shows a circle with center $O$. $MN$ is a tangent to the circle at point $S$. The angle ...
CirclesTangentsAnglesChordsGeometry
2025/4/29
We are given that triangles $HKL$ and $HIJ$ are similar. We need to find which of the given ratios i...
Similar TrianglesRatiosProportions
2025/4/29
We are given a rectangular tank with length 250 cm and width 120 cm. We pour 180 liters of water int...
VolumeRectangular PrismUnit Conversion
2025/4/29
In the given diagram, line segment $QR$ is parallel to line segment $ST$. Also, $|PQ| = |PR|$, which...
TrianglesParallel LinesIsosceles TriangleAnglesGeometric Proofs
2025/4/29
The problem asks to find the value of $m$ given that the angles $4m - 15$ and $m + 75$ are vertical ...
Vertical AnglesLinear EquationsAngle Properties
2025/4/29
We are given a quadrilateral $SPQR$ with $\angle PSR = 22^\circ$, $\angle SPQ = 58^\circ$, and $\ang...
QuadrilateralAnglesAngle Sum Property
2025/4/29
In the given circle, $S$ is the center. $JK = 4x - 2$, $LM = 10$, $SN = 8$, and $SP = 8$. $SN$ and $...
CirclesChordsGeometric ProofAlgebraic Equations
2025/4/29
We are given a circle with center $A$. We have two chords, $BE$ and $CD$. We are given that $BE = 36...
CircleChordsPythagorean TheoremRight Triangle
2025/4/29
We are given a circle with center A. We are given that $BE = 34$ and $CD = 26$. We need to find the ...
CirclesChordsPythagorean Theorem
2025/4/29
The problem asks us to find the value of $x$ given that arc $CB$ measures $115^\circ$ and is express...
GeometryArcsAnglesAlgebraic EquationsSolving for x
2025/4/29