Geometry

Problems related to shapes, spaces, measurements, etc.

Problems in this category

The problem provides two points, A(-3, 2) and (5, 7), which are joined by a line segment. We are ask...

Line SegmentMidpoint FormulaEquation of a LineSlope-Intercept FormPoint-Slope Form

The problem provides six linear equations in the form $y = mx + c$. We need to identify two equation...

Linear EquationsParallel LinesPerpendicular LinesSlopeCoordinate Geometry

In rectangle $ABCD$, $AB = 2BC$. Point $P$ is on side $AB$ such that $\angle APD = \angle DPC$. Find...

GeometryRectangleTrigonometryAngle CalculationTangentQuadratic Equation

The problem states: "The angle between the legs of a trapezoid is right. Prove that the sum of the s...

TrapezoidDiagonalsPythagorean TheoremGeometric Proof

In rectangle $ABCD$, $AB = 2BC$. On side $AB$, point $P$ is given such that $\angle APD = \angle DPC...

RectangleAnglesLaw of CosinesTrigonometry

The problem states: "The intersection points of the angle bisectors of the interior angles of a rect...

RectangleAngle BisectorSquareGeometric ProofCoordinate Geometry

Let $D, E, F$ be the points where the inscribed circle touches the sides of triangle $ABC$. Prove th...

Triangle GeometryInscribed CircleAnglesProof

Let $ABC$ be a triangle with angles $\alpha$, $\beta$, and $\gamma$. Let $X$, $Y$, and $Z$ be the po...

Triangle GeometryAngle BisectorsCircumcircleAngles in a Triangle

The problem asks us to calculate the angle between a tangent and a chord (tetiva in Serbian) if the ...

Circle GeometryTangentsChordsAngles

A circle is divided into two arcs by points A and B, and the ratio of their lengths is 5:7. We need ...

CirclesArcsAnglesCentral AnglePeripheral Angle

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