📐 geometry

1. **Problem Statement:** A chord of length 16 cm is drawn in a circle with radius 10 cm. We need to find the distance from the center of the circle to the chord.

1. **Problem statement:** We have an isosceles triangle ABC where sides AB and BC are equal in length, and side AC is parallel to the x-axis. We need to find the coordinates of poi

1. **State the problem:** We have an isosceles triangle ABC with AB = BC and side AC parallel to the x-axis. Points B and C are given as B(10, 8) and C(16, 2). Point A lies on the

1. **State the problem:** We are given a rectangle DEFG with center C at coordinates (8, 7) and point E at (20, 25). We need to find the coordinates of point G. 2. **Recall propert

1. **State the problem:** We need to find the coordinates of the center, C, of a rectangle given its bottom-left corner at $ (8, -4) $ and top-right corner at $ (16, 10) $. 2. **Fo

1. **Problem statement:** We have a pentagon DEFGH with a vertical line of symmetry at $x=7$. Points E, F, and G have coordinates $E(7,10)$, $F(11,8)$, and $G(12,0)$. We need to fi

1. **Problem Statement:** We have a pentagon DEFGH symmetric about the vertical line $x=7$. Given points are $E(7,10)$, $F(11,8)$, and $G(12,0)$. We need to find coordinates of $D$

1. **Problem Statement:** Given a parallelogram ABCD with points A(-11, 23), B(-13, 29), and C(5, 22), find the coordinates of point D. 2. **Formula and Concept:** In a parallelogr

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