Geometry
Problems related to shapes, spaces, measurements, etc.
Problems in this category
We are given a triangle ABC with side lengths $AB = 7$ cm, $AC = 4$ cm, and the angle $BAC = 80^\cir...
Law of SinesLaw of CosinesTriangleTrigonometryAngle Calculation
2025/4/21
The problem asks us to draw a triangle accurately using a ruler and protractor, given the lengths of...
Law of CosinesTrianglesTrigonometry
2025/4/21
The problem asks to construct a triangle $ABC$ with $AB = 7$ cm, $AC = 4$ cm, and angle $BAC = 80^\c...
TriangleLaw of CosinesLaw of SinesTrigonometryAngle Calculation
2025/4/21
An equilateral triangle $ABC$ has a circle inscribed within it. The radius of the circle is 4 cm. (i...
Equilateral TriangleInscribed CircleTrigonometryCyclic QuadrilateralPerimeter
2025/4/21
The problem asks us to describe the graphs of the following functions of two variables: 7. $f(x, y) ...
Multivariable Calculus3D GeometrySurfacesPlanesParaboloidsCylindersHemispheresEllipsoids
2025/4/21
In the given diagram, $WY$ and $WZ$ are straight lines, and $O$ is the center of the circle on the l...
Circle GeometryAnglesIsosceles TriangleCyclic Quadrilateral
2025/4/21
An airplane is at a horizontal distance of 1050 m from a control tower. The angles of depression fro...
TrigonometryAngles of DepressionRight TrianglesPythagorean Theorem
2025/4/21
A trapezium $PQRS$ is given, with $PQ$ parallel to $RS$. The perpendicular distance from $P$ to $RS$...
TrapeziumAreaTrigonometryAngle CalculationPythagorean Theorem
2025/4/20
The problem provides a circle $PQRS$ with center $O$. We are given that $\angle UQR = 68^\circ$, $\...
CircleCyclic QuadrilateralAnglesExterior Angle Theorem
2025/4/20
The ratio of the interior angle to the exterior angle of a regular polygon is given as $5:2$. We nee...
PolygonsInterior AnglesExterior AnglesRegular Polygons
2025/4/20