Geometry

Problems related to shapes, spaces, measurements, etc.

Problems in this category

We are given a circle with center O and a tangent line AB to the circle at point B. The length of AB...

CircleTangentPythagorean TheoremRadius
2025/5/14

We are given a triangle with a line segment that bisects an angle of the triangle. We are given the ...

TriangleAngle Bisector TheoremProportionsGeometry
2025/5/14

We are given a triangle $ABC$ with a line segment $PQ$ parallel to $BC$. We have the lengths $AP = 7...

Similar TrianglesParallel LinesProportionsTriangle
2025/5/14

The problem states that a cloth hanger is shaped like an isosceles triangle $PQR$. The angle at vert...

TriangleIsosceles TriangleAngle Properties
2025/5/14

In a circle with diameter $AOB$, $CD$ is parallel to $AB$. Given that $\angle BAD = 30^\circ$, we ne...

CirclesAnglesParallel LinesTrianglesInscribed Angles
2025/5/14

In the given figure, $AOB$ is a diameter of a circle, and $CD \parallel AB$. If $\angle BAD = 30^\ci...

CircleAnglesParallel LinesDiameterCyclic Quadrilateral
2025/5/14

In the given circle, $AOB$ is a diameter, and $CD$ is parallel to $AB$. Given that $\angle BAD = 30^...

CirclesAnglesParallel LinesDiameterQuadrilateralsTriangles
2025/5/14

Triangle ABC has sides $AB = 6.5$ cm, $BC = 7.8$ cm, and $AC = 9.1$ cm, measured to the nearest mm. ...

TrianglesPerimeterMeasurementError Bounds
2025/5/14

We are given a triangle formed by a stove, a sink, and a refrigerator. The distance between the stov...

Law of CosinesLaw of SinesTrianglesTrigonometrySide-Angle-Side (SAS)
2025/5/14

The problem asks us to find all the missing measurements of the triangle sketched in question 5. We ...

TrianglesTriangle InequalityLaw of CosinesLaw of SinesAngle-Side Relationships
2025/5/14