📐 geometry

1. **Problem statement:** Points A, B, C, D, E, and F lie on a circle with center O. Given angles are \(\angle AOB = 110^\circ\), \(\angle CDE = 10^\circ\), and \(\angle EFA = 24^\

1. **Problem statement:** Construct a triangle $\triangle ABC$ with sides $a=6.2$ cm, $b=5.5$ cm, and $c=6.5$ cm, then construct a parallelogram with one side $7$ cm whose area equ

1. **State the problem:** We are given three adjacent parallelograms with angles labeled $x$, $y$, $z$, and some known angles. We need to find the unknown values of $x$, $y$, and $

1. **State the problem:** We need to find the radius of a circle with diameter $AD$ given that $C$ lies on the circle, $B$ lies on $AC$, $E$ lies on $AD$, and $BE$ is parallel to $

1. **Problem statement:** Find all missing angles in the first circle of the first row with angles $x$, $y$, $z$, $100^\circ$, and $108^\circ$ around points $A$, $B$, $C$, $T$, and

1. **Problem statement:** A semi-circular sheet of metal with diameter 28 cm is bent into an open conical cup. Find the depth and capacity of the cup. 2. **Understanding the proble

1. **Find the value of $x$ to the nearest one decimal place.** The rectangle has a total length of 25 cm, split into segments $b$ and $x$ such that:

1. The problem asks about the location of sides labeled $a$ and $b$ in a right triangle. 2. In a right triangle, the sides are typically named as follows: the side opposite the rig

1. **Problem Statement:** Find the value of $x$ and the lengths of the sides of a right triangle where the two shorter sides are $x$ cm and $(x - 7)$ cm, and the hypotenuse is $(x

1. **State the problem:** We have a road on a map that measures 14 cm, and the scale of the map is 1 : 20,000. We need to find the actual length of the road in kilometers. 2. **Und

1. **State the problem:** We have a scale of 1 : 500, meaning 1 unit on the drawing represents 500 units in reality. 2. **Given:** Actual area = 125,000 m². We need to find the are

1. **State the problem:** We have a scale of 1 : 500, meaning 1 unit on the drawing represents 500 units in reality. 2. **Given:** Actual area = 125,000 m². We want to find the are

1. **Problem Statement:** Construct triangle XYZ with sides |YZ| = 6 cm, |ZX| = 6 cm, and |ZY| = 9 cm, and angle YZX = 60°.

1. **State the problem:** We need to find the size of angle $x$ in a right triangle with sides 9.7 cm (vertical) and 5.1 cm (horizontal). 2. **Formula used:** To find an angle in a

1. **State the problem:** We have a scale drawing of a classroom with dimensions 9.6 cm by 7.2 cm, drawn at a scale of 1 : 75. We need to find the actual dimensions of the classroo

1. **State the problem:** We need to find the arc measure of the minor arc \(\stackrel{\large{\frown}}{BC}\) in degrees on a circle centered at point P with points A, B, C, and D o

1. **State the problem:** We have a scale of 1 : 1000, meaning 1 unit on the drawing represents 1000 units in reality. 2. **Given:** Actual distance between two villages is 2.4 km.

1. The problem asks to find the image that is different as a result of reflection among the given options. 2. Reflection means flipping a figure over a line (mirror line) so that t

1. Stating the problem: We need to find the volume and surface area of two vertical cylinders. 2. Formula for a cylinder:

1. **State the problem:** We have a rectangular garden measuring 30 m by 18 m, drawn to a scale of 1 : 300. We need to find the dimensions of the drawing in cm and then calculate t

1. The problem asks: "An inscribed angle is an angle with its vertex on the _____________ of the circle." The correct answer is "edge" or "circumference" because an inscribed angle