📐 geometry

1. Stating the problem: We are given two points, P(-2, -2) and Q(x, 2), and the length of the line segment PQ is 5 units. 2. Use the distance formula between two points $P(x_1, y_1

1. The problem asks for the length of a line segment with endpoints at coordinates $(1,2)$ and $(5,6)$ on the Cartesian plane. 2. To find the length of a line segment between point

1. **State the problem:** We are given points $A=(-5,5)$ and $B=(3,7)$ and must find point $P$ on the y-axis such that $P$ is equidistant from $A$ and $B$. 2. **Analyze the problem

1. Given a rhombus with diagonals intersecting at the center, one half of the horizontal diagonal is $2.5$ units and one half of the vertical diagonal is $5.5$ units. 2. The length

1. הבעיה: יש לנו יהלום שמחולק לארבעה משולשים על ידי שתי קווים ניצבים. 2. ניתן לראות שהזווית העליונה ימנית היא $45^\circ$.

1. Stating the problem: We have a circular park with pathways connecting the main road to gates and an exit. 2. Given: Distance from main road to Gate 2 is 70 m and the path from G

1. The problem describes a graph with points labeled 96, 137, 111.99, 80.90, 1440, and 25.10 related to labels "H.T.T" and "M25.10" connected by line segments and curves resembling

1. We are given a set of angle options: 10, 66, 165, 115, and 135 degrees. 2. To find possible mixes or matches, we might consider sums, differences, or relationships such as suppl

1. **Statement of the problem:** We are given four geometric setups involving angles labeled with expressions in terms of $x$, $y$, $z$, and some numerical angles. We need to find

1. **State the problem:** We need to find the midpoints of the line segments AB, EF, and CE, and the distances between points AC, BC, AF, and DF given the points:

1. **Stating the problem:** In triangle AABC, the sides are given by AB = $x$ cm, BC = 5 cm, and AC = $(10 - x)$ cm. We need to:

1. Find the measure of arc QS given angle at tangent Q is 128°. The angle formed between a tangent and a chord is half the measure of the intercepted arc.

1. **State the problem:** We need to find the volume of a rectangular prism with length $l = 8$ cm, width $w = 3$ cm, and height $h = 5$ cm. 2. **Understand the formula:** The volu

1. **Problem 1 setup:** Given the equation:

1. **State the problem:** We have a circle with an inscribed triangle PQR, where the angles at points near P are 46° and 70°. 2. **Identify given angles:** Angle QPR is adjacent to

1. **Stating the problem:** We need to find the value of angle $k$ in several geometric configurations involving circles, tangents, and cyclic quadrilaterals, using given data such

1. The problem: Calculate the volume of a sphere given its radius. 2. The formula for the volume of a sphere is $$V=\frac{4}{3}\pi r^{3}$$ where $r$ is the radius.

1. It seems like you're asking about how to determine or calculate the length in a given problem. 2. To help you precisely, please provide the specific problem or context involving

1. The question "What about length?" is a bit broad, so let's clarify what kind of length you're asking about. 2. If this relates to a math problem or geometric figure, length usua

1. We are given a triangle △ABC and need to construct a triangle similar to △ABC whose sides are $\frac{8}{5}$ times the corresponding sides of △ABC. 2. To do this, draw a ray BX s

1. **Find the perimeter of diagram Q consisting of four identical right-angled triangles each with sides 3 cm, 4 cm, and 5 cm.** 2. Each triangle has sides 3 cm, 4 cm, and hypotenu