📐 geometry

1. **State the problem:** We are given a circle H with angles \(m\angle DHG = 11x - 36\) and \(m\angle GHF = 3x + 12\). We need to find the value of \(x\) and the measure of \(\ang

1. **State the problem:** We need to find the volume of a composite solid made of a cone on top of a cylinder. 2. **Given:**

1. **State the problem:** We are given the endpoints of a diameter of a circle at points $(3,4)$ and $(5,-2)$, and we need to find the radius of the circle. 2. **Recall the formula

1. **State the problem:** We need to determine which points lie on the circle with center $O(2,3)$ and radius $4$. 2. **Formula:** The equation of a circle with center $(h,k)$ and

1. **State the problem:** We are given three angles on a straight line labeled as $3x^\circ$, $x^\circ$, and $2x^\circ$. We need to find the value of $x$. 2. **Formula and rule:**

1. **Problem Statement:** Find the correct ordered pair location of the fourth vertex of the rhombus given vertices and hints. 2. **Given Information:** The rhombus has vertices wi

1. **State the problem:** We have a rhombus, and the slope of one diagonal is $\frac{2}{3}$. We need to find the slope of the other diagonal. 2. **Recall properties of a rhombus:**

1. Задачата не е напълно ясна, но изглежда се отнася до свързване на точки с точка А с оригиналните числа. 2. Ако имаме точка А и други точки с координати, свързваме ги чрез линии,

1. **Problem:** A circle has an area of $289\pi$ cm$^2$. Find the approximate circumference. 2. **Formula:** Area of a circle is $A = \pi r^2$.

1. **Nêu bài toán:** Từ điểm $A$ nằm ngoài đường tròn $(O;R)$, vẽ hai tiếp tuyến $AB$ và $AC$ với $B, C$ là các tiếp điểm. Vẽ đường kính $BD$ của đường tròn $(O)$. Gọi $K$ là hình

1. **State the problem:** We have a triangle with vertices at $(1, 2)$, $(1, 6)$, and $(4, 4)$. We want to find which transformation sequence results in the same triangle with vert

1. The problem asks to identify all shapes similar to triangle T. 2. Similar triangles have the same shape but may differ in size. This means their corresponding angles are equal a

1. The problem asks to identify all triangles similar to triangle T in the given diagram. 2. Two triangles are similar if their corresponding angles are equal and their correspondi

1. **Problem statement:** We have two concentric circles with center $O$. Points $A, B, C, D$ lie on the outer circle, and $E$ lies on the inner circle. Lines $\overline{ABCD}$ and

1. The problem asks to categorize triangles based on their angles: acute, obtuse, or right. 2. Definitions:

1. The problem asks to categorize six triangles based on their angles: acute, obtuse, or right. 2. Recall the definitions:

1. **Stating the problem:** We need to categorize triangles based on their angles into three groups: triangles with all acute angles, triangles with an obtuse angle, and triangles

1. The problem is to categorize triangles based on their angle types: acute, obtuse, or right. 2. Definitions:

1. The problem asks to identify a true property of a figure correctly placed in the shaded red section of a classification diagram of quadrilaterals. 2. The diagram shows nested ca

1. **State the problem:** We need to find the surface area of a shape, but the shape is not specified. Assuming the problem is to find the surface area of a sphere (a common surfac

1. **State the problem:** We need to find the surface area of a cylinder with height $7m$ and radius $9m$. 2. **Formula for surface area of a cylinder:**