📐 geometry

1. **State the problem:** Find the coordinates of a point on the y-axis that is equidistant from the points $(4,-2)$ and $(4,6)$. 2. **Recall the formula:** The distance between tw

1. **Problem statement:** We are given a circle centered at $(0,0)$ with an area of $9\pi$. We need to determine which point the circle does not pass through. 2. **Formula for the

1. **State the problem:** We need to find the surface area of a rectangular prism with dimensions 5 units by 5 units by 8 units, where two faces have curved edges forming semicircl

1. The problem is to find the volume or surface area of a quarter cylinder, which is one-fourth of a full cylinder. 2. Recall the formulas for a full cylinder:

1. **Problem Statement:** Find the surface area of a semicylindrical solid with radius $r=5$ cm and length $l=8$ cm.

1. **Stating the problem:** We have a cuboid with volume 360 cm³ and surface area A cm².

1. **Stating the problem:** We want to find the area $A$ of a triangle given its base $b$ and height $L$. 2. **Formula used:** The area of a triangle is calculated by the formula:

1. **Problem Statement:** Reflect the polygon ABCD with vertices A(2, -2), B(-2, 2), C(0, 4), and D(4, 0) across the line $y = x$. 2. **Reflection Formula:** When reflecting a poin

1. **Problem Statement:** We have a benchmark blob with area $b$ cm$^2$. We need to estimate the areas of four different shapes in terms of $b$. 2. **Understanding the Problem:** T

1. **Problem statement:** We have a right-angled triangle ABC with right angle at B. AB is parallel to ED. The areas of triangles EDC and BED are 24 cm² and 72 cm² respectively. We

1. **Problem Statement:** In triangle $\triangle DEF$, point $C$ is the centroid. Given that $HD = 30x - 6y$, find the expression for $CD$.

1. **Problem Statement:** Identify a median in triangle $\triangle GBI$ using the given figure. 2. **Definition of a Median:** A median of a triangle is a line segment joining a ve

1. **Problem Statement:** We are given triangle $PQR$ with altitudes $\overline{RS}$ and $\overline{PT}$ drawn from vertices $R$ and $P$ respectively. The measure of angle $Q$ is $

1. **Problem Statement:** We are given a right triangle $\triangle ABC$ with a right angle at $A$. Points $K$ and $Q$ lie on segments $AB$ and $AC$ respectively. Segment $BK$ is gi

1. The problem asks for the size of the reflex angle given the smaller angle is approximately 50 degrees. 2. Recall that a reflex angle is the larger angle formed by two lines, whi

1. **State the problem:** We are given a circle divided into four sectors with central angles 18°, $x$, $2x$, and 147°. We need to find the value of $x$. 2. **Formula and rule:** T

1. **State the problem:** We have a circle divided into two parts: a green sector measuring 174° and an orange sector divided into three equal smaller sectors each labeled $k$. We

1. **Problem Statement:** We are given a square on the Cartesian plane with vertices A(2,2), B(6,2), C(6,-2), and D(2,-2). We want to analyze the properties of this square, such as

1. **State the problem:** We have a right triangle with a vertical side of length $n$ and a horizontal side of length 20. We want to understand the relationship between these sides

1. **Problem Statement:** We are given different scales and lengths on maps or plans and need to find actual lengths or map lengths using the scale.

1. **Problem Statement:** We are given a scale of 1:500000 and a drawn length of 15 cm. We need to find the actual length represented by this drawn length.