Geometry
Problems related to shapes, spaces, measurements, etc.
Problems in this category
The problem asks us to calculate the peripheral angle (also known as the inscribed angle) above a ci...
CircleAnglesInscribed AngleCentral AngleArc
2025/3/29
We are given a circle and three points $A, B, C$ on the circle which divide the circle into three ar...
CircleTriangleInscribed AngleArc Length
2025/3/29
The problem states that three interior angles of a quadrilateral are $75^{\circ}$, $105^{\circ}$, an...
QuadrilateralsCirclesCyclic QuadrilateralsAngle Properties
2025/3/29
In triangle $ABC$, the angle bisectors of angles $\alpha$ and $\gamma$ intersect at point $M$. Calcu...
TriangleAngle BisectorAngle Calculation
2025/3/29
The image shows a rectangle ABCD with length $4x+y$ cm and width $4x$ cm. We are asked to find: (a) ...
RectangleAreaPerimeterTriangleAlgebra
2025/3/29
The problem states that BD is a diagonal of a rectangle and it divides the rectangle into two equal ...
AreaRectangleTriangleDiagonal
2025/3/29
In triangle $ABC$, the angle bisectors of angles $\alpha$ and $\gamma$ intersect at point $M$. Calcu...
TrianglesAngle BisectorsAngle CalculationGeometry
2025/3/29
Given triangle $ABC$, the exterior angle at vertex $A$ is $134^\circ$ and the interior angle at vert...
TrianglesAnglesAngle BisectorsInterior AnglesExterior Angles
2025/3/29
Triangle $ABC$ is an isosceles triangle with $AC = BC$. Point $D$ lies on the extension of side $AC$...
TrianglesIsosceles TriangleAnglesProof
2025/3/29
We are given a triangle where one of the angles is $\frac{2}{5}$ of the second angle and $\frac{1}{4...
TrianglesAnglesAlgebraSolving Equations
2025/3/29