📐 geometry

1. **State the problem:** We have a square with an area of 225 cm², and we want to find the radius $r$ of the largest circle that can fit inside the square. 2. **Recall the formula

1. **Problem statement:** Given two parallel lines $\ell \parallel m$, and $\overrightarrow{DE}$ bisects $\angle CDF$, find the value of $y$. 2. **Understanding the problem:** Sinc

1. **Problem statement:** Given two parallel lines $l \parallel m$, and a ray $\overrightarrow{DE}$ that bisects $\angle CDF$, find the value of $y$. 2. **Understanding the problem

1. **Problem:** Find the length of segment NM in a circle with center K and radius 16. Points L and N lie on the circumference, M is outside the circle. Line segment MN intersects

1. **Problem:** Find the length of segment NM given that segments KL and MN are parts of chord KM in a circle, with lengths $x - 3$ and $x + 3$ respectively, and the entire chord K

1. **Problem statement:** We have an equilateral triangle QPR, and we are given that angle PRS equals $2x - 10^\circ$. We need to find the value of $x$. 2. **Important properties:*

1. The problem asks to identify an angle that is greater than 180° but less than 360°. 2. Angles are measured in degrees, and a full circle is 360°.

1. The problem asks to find an angle that is greater than 189° but less than 360°. 2. Angles are measured in degrees, and the range given is between 189° and 360°.

1. **State the problem:** We have a map scale of 1:100,000, meaning 1 cm on the map represents 100,000 cm in reality. 2. **Formula and explanation:** The real distance $D$ is given

1. The problem is to find unknown angles in various polygons: triangle, square, rhombus, kite, and quadrilateral. 2. Important formulas and rules:

1. **Problem Statement:** Find the measures of angles (a) $\angle ADX$, (b) $\angle ABC$, and (c) $\angle BCD$ given the circle with points $A$, $B$, $C$ on the circumference, poin

1. **State the problem:** We are given that the sum of the interior angles of a regular polygon is 1440 degrees. We need to find the size of each exterior angle of this polygon. 2.

1. The problem is to understand and apply the circle theorem. 2. One common circle theorem states: "The angle subtended by a diameter at the circumference is a right angle."

1. **Problem statement:** Given a right-angled triangle with an angle $\Omega = 55^\circ$ and a circle of diameter $D = 20$ mm inscribed such that it is tangent to the hypotenuse a

1. **Problem statement:** Given a circle with tangent segments VQ and VK, and a line segment IK, where $QV=8$ cm, $IK=24$ cm, and $KV=x$ cm, find the value of $x$. 2. **Key propert

1. **Problem statement:** Four congruent rectangles are arranged to form an inner square of area $20$ cm² and an outer square of area $64$ cm². We need to find the perimeter of one

1. **Problem statement:** The shape is a rectangle with a notch on top. The total perimeter is 60 cm. The rectangle's height is 8 cm, the bottom length is 18 cm, and the notch widt

1. **Problem Statement:** Meg is playing with a toy shaped like a hexagonal prism divided into six triangular faces. Three alternate triangular faces are shaded, each with a white

1. **Stating the problem:** Encik Hamid wants to plant 18 oil palm trees arranged so that the distance between each tree is 9 m, and the planting pattern forms an equilateral trian

1. **State the problem:** Find the area of the irregular polygon composed of three rectangles stacked like steps, with all sides meeting at right angles. 2. **Identify the shapes a

1. **Problem statement:** Find the total surface area of a right pyramid VABCD with a rectangular base of length 16 cm and width 14 cm, and slant edge length 25 cm. 2. **Formula an