Geometry
Problems related to shapes, spaces, measurements, etc.
Problems in this category
We are given a circle with equation $x^2 + y^2 + 2x - 6y + 1 = 0$ and a line with equation $3x - y +...
CirclesLinesChordMidpointDistance FormulaCoordinate Geometry
2025/4/28
The problem asks to identify a central angle in a circle with center $F$. $GI$ is a diameter and the...
CircleCentral AngleDiameterSupplementary Angles
2025/4/28
We are given a circle with center $T$. $NL$ and $MK$ are diameters of the circle. We are given that ...
CirclesAnglesArcsDiametersCentral AngleMajor Arc
2025/4/28
The problem asks us to identify the type of arc $mNL$ (major arc, minor arc, or semicircle) and find...
CircleArcDiameterCentral AngleMajor ArcMinor Arc
2025/4/28
We are given a circle with center $T$. $NL$ and $MK$ are diameters of circle $T$. In Part A, we need...
CirclesArcsAnglesDiameterMajor ArcMinor ArcSemicircle
2025/4/28
The problem asks to find the value of $x$ given that a circle is divided into three angles: $189^\ci...
AnglesCirclesEquation Solving
2025/4/28
Calculate the area of a regular dodecagon with a radius of 5 cm.
AreaPolygonsDodecagonTrigonometryRegular Polygon
2025/4/28
A hollow hemispherical bowl A has an inner radius of $a$ cm and a thickness of 1 cm. There is also a...
Surface AreaHemisphereArea CalculationGeometric Shapes
2025/4/28
The problem requires us to find the lengths of sides $b$ and $c$ in a right-angled triangle ABC, whe...
TrigonometryRight TrianglesSineCosineTriangle Sides
2025/4/28
We are given a right triangle $ABC$ with a right angle at vertex $A$. We are given the length of sid...
TrigonometryRight TrianglesCosineSide Length Calculation
2025/4/28