📐 geometry

1. **State the problem:** We are given a rectangle ABCD with vertices A(-7, 8), B(3, 8), C(-7, -6), and D(3, -6). We need to find: a) The perimeter of the rectangle.

1. **State the problem:** We have a rectangle DEFG with points E(3, 2) and G(-1, -5) given. The sides of the rectangle are parallel to the axes, and we need to find the coordinates

1. **State the problem:** Calculate the area of the triangle with vertices at points (3, 1), (9, 1), and (7, 8). 2. **Formula for the area of a triangle:**

1. **Problem Statement:** We have a quadrilateral ABCD with arcs drawn at each vertex A, B, C, and D. Each arc has a radius of 7 cm and is centered at the respective vertex. We nee

1. The problem is to identify or work with the point $(2,2)$ in the coordinate plane. 2. A point in the coordinate plane is represented as $(x,y)$ where $x$ is the horizontal coord

1. **Problem statement:** Given an isosceles triangle $\triangle ABC$ with $|AB|=|AC|=6$ cm and $|BC|=4$ cm, find the points equidistant from $B$ and $C$ and 3 cm from $A$, then me

1. **Problem Statement:** Find the values of $x$ and $y$ in the parallelogram with side lengths labeled as $2x + 2$, $2y + 2$, $3x - 7$, and $3y - 11$. 2. **Key Property:** In a pa

1. **Problem Statement:** ABCD is a rhombus and P, Q, R, and S are the mid-points of sides AB, BC, CD, and DA respectively. Show that quadrilateral PQRS is a rectangle. 2. **Formul

1. مسئله: ما باید حاصل جمع دو کمان \overarc{AB} و \overarc{CD} را پیدا کنیم که هر دو کمان از یک دایره با مرکز O هستند. 2. اطلاعات داده شده:

1. **Stating the problem:** We have an irregular L-shaped polygon with given side lengths: bottom horizontal length 32 cm, left vertical height 22 cm, top left horizontal segment 8

1. **Problem statement:** Find the radius $r$ of each circle given the perimeter or area of minor or major arcs/sectors. 2. **Formulas and rules:**

1. **Problem statement:** We have a circle with center O and radius 6 cm. Two radii OA and OD form an angle of 62°. Points B and C lie on the circle such that AB = DC = 5 cm outsid

1. **Problem:** Find three different rectangular prisms each with surface area 72 square units. 2. **Formula:** Surface area of a rectangular prism with length $l$, width $w$, and

1. **Problem Statement:** We have a rectangular prism with surface area 80 square units. The prism shown is 5 units long, 4 units wide, and 2 units high. We want to find other rect

1. **Stating the problem:** We have a cone with height 120 cm and base diameter 80 cm (thus radius 40 cm). Inside it, a cylinder is inscribed with height $h$ and radius $r$. We wan

1. The problem states that we have a point $A$ with coordinates $(3,1,2)$ in 3D space. 2. This is a straightforward identification of a point in three-dimensional Cartesian coordin

1. დავიწყოთ ამოცანის დასმით: იპოვოთ კუთხე \(\angle ABC\), თუ \(\angle ABC = 260^\circ\).\n\n2. აქ მოცემულია, რომ \(\angle ABC\) უკვე არის 260 გრადუსი, რაც არ არის ჩვეულებრივი კუთხი

1. The problem asks to find the distance between the centers of two circles with radii 5 cm and 8 cm, respectively. 2. When two circles are tangent externally, the distance between

1. The problem is to understand the properties and calculations related to triangles. 2. A triangle is a polygon with three edges and three vertices.

1. The problem is to understand what polygons are and their basic properties. 2. A polygon is a closed plane figure with at least three straight sides and angles.

1. **Stating the problem:** We are given a circle with center $O$, chords $AB$ and $AC$ equal in length, and point $E$ on the extension of $AO$ intersecting chord $DC$. We need to