📐 geometry

1. **Problem Statement:** Find the missing value of Surface area ÷ Volume for a cube stack with 27 cubes.

1. The problem is to find the distance between two points in a plane using the distance formula. 2. The distance formula between points $A(x_1,y_1)$ and $B(x_2,y_2)$ is:

1. **Problem:** On a circle of radius 10 m, find the length of an arc subtending a central angle of (a) $\frac{4\pi}{5}$ radians, (b) 110°. 2. **Formula:** Arc length $s$ is given

1. **Problem Statement:** Prove that the angle between the two tangents drawn from an external point to a circle is supplementary to the angle subtended by the line segment joining

1. **State the problem:** We have two vertical parallel lines cut by a transversal. Given angles 30°, 134°, and 110° on the left line, and angles $x^\circ$ and $y^\circ$ on the rig

1. **Problem statement:** We have an isosceles triangle ABC with vertex A and base BC.

1. **Problem statement:** Given a circle with points A, B, C, D, E on the circumference and center O, with EOB a straight line, \(\angle AÔB = 105^\circ\) and \(\angle BÊC = 20^\ci

1. **Problem statement:** Given \(\angle ABP = 76^\circ\), find the value of \(y\) in the figure. 2. **Relevant concept:** In circle geometry, the angle formed outside the circle b

1. The problem is to analyze the given figure and solve the first question related to it. 2. Since the figure is not provided in text, please describe the problem or provide the fi

1. **Problem statement:** We need to find how many triangles are formed in a trapezoid divided into four horizontal layers by three parallel lines, with one diagonal from the top-l

1. **Stating the problem:** We need to find how many triangles are in the given geometric figure, which is a large triangle subdivided by three segments connecting vertices to poin

1. **Problem statement:** We have a table with a circular top and a circular base.

1. **Problem statement:** We have a solid cut into two identical halves along the plane of symmetry VAFHCV. We need to calculate the surface area of one of these halves. 2. **Under

1. **State the problem:** Calculate the volume of a solid consisting of a rectangular block with a square base of side length 6 cm and height 10 cm, topped by a right pyramid with

1. **Stating the problem:** We have an obtuse angle $x\hat{O}y$ with vertex $O$. The bisector of this angle is the semi-line $[Ou]$. Points $F$ and $R$ lie on $[OY]$ and $[OX]$ res

1. **State the problem:** We will list and explain all 9 circle theorems, which are fundamental properties relating angles, chords, tangents, and segments in a circle. 2. **Theorem

1. The problem is to understand and list all the main circle theorems. 2. Circle theorems are rules about angles, lengths, and arcs in circles that help solve geometry problems.

1. **Problem statement:** Given a circle with center $O$, a tangent line $BCD$ touching the circle at point $C$, and a point $A$ on the circle, prove that $\angle BAC + \angle ACD

1. The problem is to find the formula for the area of a circle. 2. The area of a circle is the amount of space enclosed within its boundary.

1. **Постановка задачи:** Даны секущие EA и EB, пересекающие окружность с центром в точке O, и хорда CD. Известно, что $AB=AE$ и $BE=12$. Нужно найти длину хорды $CD$. 2. **Формула

1. **State the problem:** We need to find the length of the hypotenuse $QR$ in a right triangle $PQR$ where the right angle is at $P$. The sides adjacent to the right angle are $PQ