📐 geometry

1. The problem involves calculating perimeters or circumferences based on given dimensions. 2. The formulas for each shape are:

1. **State the problem:** Calculate the circle's circumference, the square's perimeter, and the parallelogram's perimeter given:

1. **Énoncé du problème :** Nous avons la droite $\mathcal{D}$ d'équation $3x + 4y - 8 = 0$ et un point $A(2;3)$. Nous voulons écrire une fonction Python qui teste si un point $M(x

1. The problem is to find the measure of the missing angle in a triangle where the other two angles are given as 76° and 56°. 2. The formula used is the Triangle Angle Sum Theorem,

1. The problem is to find the measure of the missing angle in a triangle where the other two angles are given as 149° and 87°. 2. The formula used is the Triangle Angle Sum Theorem

1. The problem asks to identify the name given to the repeating pattern formed by the shapes shown in the diagram. 2. The diagram shows a sequence of interconnected rhombus shapes

1. **State the problem:** We have a trapezoid with the top base labeled as $-4w + 46$, the bottom base as $22$, and the two non-parallel sides marked equal, meaning the trapezoid i

1. **State the problem:** We have a circle defined by the equation $$x^2 + y^2 = 25$$. 2. **Find the centre and radius:** The general form of a circle equation is $$ (x - h)^2 + (y

1. **State the problem:** We have two parallel lines $m$ and $n$ cut by a transversal. The angles given are $(9x - 13)^\circ$ on line $m$, $(3x - 11)^\circ$ on line $n$, and an adj

1. **State the problem:** We have two parallel lines $m$ and $n$ cut by a transversal, creating angles labeled as $(9x+2)^\circ$, $(5x-18)^\circ$ near line $m$, and $(2y+20)^\circ$

1. مسئله: در شکل داده شده، باید حداقل چند چوب کبریت حذف کنیم تا دقیقاً سه مثلث در شکل باقی بماند، بدون اینکه چوب کبریتی اضافه بماند. 2. توضیح: هر مثلث از سه ضلع تشکیل شده است. حذف

1. **Stating the problem:** Find the measure of the angle marked with a letter in diagram 2(e), where angles 91° and 36° are given in a figure with points A, B, C, D, E.

1. Problem 26: Given a right triangle with hypotenuse 9, legs $x$ and $y$, find $x$ and $y$. 2. Use the Pythagorean theorem: $$x^2 + y^2 = 9^2 = 81$$

1. **Stating the problem:** We have a quadrilateral with vertices A(-8,-3), B(13,-3), C(8,9), D(-3,9). We need to represent it on a Cartesian plane, identify the polygon, calculate

1. **Problem statement:** In triangle $ABC$, $AD$ is perpendicular to $BC$ and satisfies the relation $AD^2 = BD \times DC$. We need to prove that $\angle BAC = 90^\circ$. 2. **Giv

1. **Stating the problem:** We have a polygon with vertices at points $(1,9)$, $(4,9)$, $(4,7)$, $(2,4)$, and $(2,1)$. We want to increase its size by a factor of $\frac{3}{2}$. Th

1. **State the problem:** We are given a triangle ABC with sides AC = $7\sqrt{3}$ cm, AB = $\sqrt{6}$ cm, and BC = $a$ cm. The angle at vertex A is 45°. We need to show that $a = \

1. **State the problem:** We have a right triangle with a hypotenuse of length 8.5, and the base is divided into two segments of lengths 3.2 and 6.8 by a height $x$ perpendicular t

1. **State the problem:** We need to find the value of $\cos E$ in a right triangle $EFG$ where the right angle is at vertex $F$. The sides adjacent to $F$ are $EF = 18$ and $FG =

1. **State the problem:** We have a rectangular prism ABCDEFGH with the sum of all edge lengths equal to 28 cm and total surface area equal to 13 cm². We need to find the length of

1. **State the problem:** We have a rectangular prism ABCDEFGH with the sum of all edge lengths equal to 28 cm and total surface area equal to 13 cm². We need to find the length of