📐 geometry

1. The problem asks for the order of rotational symmetry of a shape that looks like a three-pointed star or propeller. 2. Rotational symmetry order is the number of times a shape f

1. **Problem statement:** We have a circle with center $O$ and points $A$, $B$, $C$, and $D$ on the circumference. $FDE$ is a tangent line touching the circle at $D$. We are given

1. **Problem statement:** We need to find the area of the shaded segment of a circle. The sector has radius $r=16$ cm and central angle $\theta=140.3^\circ$. The chord length is 30

1. **Problem statement:** Find the coordinates of point P which is 5 cm from BC and 4 cm from A's altitude in rectangle ABCD with AB = 8 cm and BC = 6 cm. 2. **Formula and rules:**

1. **Problem:** Given a circle with center O, angles \(\angle OAB = 30^\circ\) and \(\angle OCB = 40^\circ\), find \(\angle AOC\). 2. **Formula and rules:** In a circle, the angle

1. The problem asks to find the result of translating point R(-5,8) by the translation vector T = [-3,-4]. 2. The formula for translation is:

1. **Stating the problem:** We have a right triangle RST with a right angle at vertex S.

1. **State the problem:** We need to prove that the tangent line ABC at point B is parallel to the chord EF of the circle. 2. **Given:**

1. **State the problem:** We need to prove that the tangent line ABC at point B is parallel to the chord EF of the circle. 2. **Given:**

1. **State the problem:** We are given points A(2, -2), B(2, 3), C(-1, 5), and D(-1, 0) which form a parallelogram ABCD. We need to find the perimeter of this parallelogram. 2. **R

1. **State the problem:** We are given three points $N(-3,1)$, $O(-3,-7)$, and $P(1,-5)$ that form a triangle. We need to find the perimeter of this triangle. 2. **Recall the formu

1. **Stating the problem:** We need to find the area of rectangles using the formula $$A = r \times b$$ where $r$ and $b$ are the lengths of the sides.

1. **State the problem:** Find the area of rectangles using the formula $$A = l \times b$$ and find the actual area when $$l=3$$ cm and $$b=1$$ cm.

1. **State the problem:** We have a right-angled triangle with adjacent sides of lengths $x$ cm and $(x-1)$ cm, and the hypotenuse length is $\sqrt{13}$ cm. We need to find the val

1. **Énoncé du problème :** Soit le triangle EFG avec EF = 5 cm, EG = 4 cm, FG = 3 cm. Le point M est sur le segment [EG] tel que EM = 6 cm. Une droite parallèle à (FG) passant par

1. **Énoncé du problème :** Calculer EN et MN dans le triangle EFG où EF = 5 cm, EG = 4 cm, FG = 3 cm, M est un point sur [EG] tel que EM = 6 cm, et la droite passant par M et para

1. **Énoncé du problème :** Calculer les longueurs EN et MN dans le triangle EFG où EF = 5 cm, EG = 4 cm, FG = 3 cm, et M est un point sur [EG] tel que EM = 6 cm. Une droite parall

1. **State the problem:** We have a circle with center $O$ and diameter $FG$. The arc $FXG$ has length $14\pi$. We need to find the length of the line segment $XO$. 2. **Understand

1. **Stating the problem:** We are given a geometric figure with points V, A, B, C, M, N, X, and Y.

1. **State the problem:** We are given the circumference of a plastic pipe as $4 \frac{1}{2}$ inches and the pipe thickness as $\frac{1}{16}$ inch. We need to find the inside diame

1. **State the problem:** A customer gives the circumference of a tire's wheel rim as 44 inches. We need to find the approximate diameter of the tire.