📐 geometry

1. **Énoncé du problème :** On considère un triangle ABC avec (EF) parallèle à (BC), et les longueurs suivantes : $AC=4$, $BC=5$, $EA=12$, $AB=3$.

1. **Stating the problem:** We want to find the coordinates of point P that divides the line segment AB in the ratio $m:n$.

1. **Problem statement:** Given circle Q with \(\overline{MN} \cong \overline{OP}\) and radius 12 units, find the measure of \(\angle 4\). 2. **Relevant formula and rules:** In a c

1. **Stating the problem:** We need to find the measure of angle $\angle xyb$ given that $\angle xyb$ is formed by a line segment from point $y$ to $x$ making a $15^\circ$ angle wi

1. **Stating the problem:** We are given a horizontal line with points A, C, and B, and a line from point C forming a 60° angle with the horizontal. We need to find the measure of

1. **State the problem:** We are given an arc length $s = 30$ cm and a central angle $\theta = 120^\circ$ in a circle. We need to find the radius $r$ of the circle. 2. **Formula us

1. **Problem statement:** We have a circle with center $O$ and a circumscribed angle $A$ around it. We want to find the length of segment $\overline{AB}$. Given are an angle of $73

1. **Problem statement:** We have a circle with center $O$ and a circumscribed angle $A$ around it. We want to find the length of segment $\overline{AB}$. Given are an angle of $73

1. The problem asks for the coordinates of the two labeled points on the graph. 2. From the description:

1. **Problem:** What is an angle whose vertex is on a circle and whose sides contain chords of the circle? 2. **Definition:** An inscribed angle is an angle whose vertex lies on th

1. **Problem statement:** We have an equilateral triangle $\triangle ABC$ inscribed in a circle $\omega_1$ with radius 4. Another circle $\omega_2$ with radius 2 is tangent interna

1. **State the problem:** Find the midpoint of the line segment joining the points (8, -6) and (4, 5). 2. **Formula:** The midpoint $M$ of a segment with endpoints $(x_1, y_1)$ and

1. The problem asks to find the distance between the points $(15,11)$ and $(33,36)$. 2. We use the distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$:

1. **Stating the problem:** We have two points describing a mountain climbing expedition: Point A at (11,200 meters east, 3,200 meters above base camp) and Point B at (8,400 meters

1. **State the problem:** We are given two angles formed by a transversal crossing two parallel lines. The angles are \( (85 - 2x)^\circ \) and \( (93 - 4x)^\circ \). We need to so

1. **State the problem:** We need to find the measure of angle $\angle RTN$ given two expressions for angles formed by two parallel lines cut by a transversal: one angle is $(55 -

1. **State the problem:** Find the area of the compound figure composed of rectangles and triangles with given side lengths. 2. **Analyze the figure:** The figure can be divided in

1. **State the problem:** We have a right triangle with one leg measuring 132 cm and the hypotenuse measuring 165 cm. We need to find the length of the other leg. 2. **Formula used

1. The problem asks to identify the highlighted part of circle O, where O is the center of the circle and the shaded region is between points O and S. 2. In circle geometry, a **se

1. The problem asks to identify the highlighted part of circle O. 2. Important definitions:

1. **Problem statement:** Given that \(\overline{AD} \parallel \overline{EG}\), \(\overline{BH} \perp \overline{FC}\), and \(m\angle ABH = 149^\circ\), find \(m\angle EFH\). 2. **I