Geometry
Problems related to shapes, spaces, measurements, etc.
Problems in this category
The problem asks to calculate the area of a regular polygon circumscribed about a circle, given that...
PolygonsAreaPerimeterCircumscribedLimits
2025/3/27
The problem states "Доказать особину средње линије троугла" which translates to "Prove the property ...
TriangleMidlineParallel LinesSimilaritySAS Similarity
2025/3/27
Point $M$ is the midpoint of side $BC$ of triangle $ABC$. Prove that $\vec{AB} + \vec{AC} = 2\vec{AM...
VectorsTriangleMidpointVector AdditionGeometric Proof
2025/3/27
Given vector $\vec{a}=(1, \sqrt{3})$ and the angle between $\vec{a}$ and $\vec{b}$ is $\frac{\pi}{6}...
VectorsProjectionsDot ProductTrigonometry
2025/3/27
The given equation is $x^2 = 4py$. We are asked to solve this problem. Since there are no further in...
ParabolaConic SectionsEquation of a ParabolaFocusDirectrixLatus Rectum
2025/3/27
The problem states that a side of a triangle has been extended to form an exterior angle of $122^\ci...
TrianglesExterior AnglesRight TrianglesAngle Properties
2025/3/27
We are given two triangles, $\triangle JKL$ and $\triangle ZYX$. We are given that $\overline{JK} \c...
Triangle CongruenceSAS CongruenceSSS CongruenceGeometric Proofs
2025/3/27
We are given two triangles. One is a right triangle, and the other is an isosceles triangle. The eq...
TrianglesCongruenceRight TriangleIsosceles TriangleTriangle Congruence Theorems
2025/3/27
We are given two intersecting lines. One angle is labeled as $123^\circ$ and the angle adjacent to i...
AnglesLinear EquationsSupplementary AnglesAlgebra
2025/3/27
The problem asks to find the measure of angle $PNO$. We are given that the measure of angle $ONM$ is...
AnglesTriangle PropertiesAngle Measurement
2025/3/27