📐 geometry

1. The problem states that we have a circle with radius $\frac{4}{9}$ units and center at $(-6.2, 5.8)$. 2. The general equation for a circle with center $(h, k)$ and radius $r$ is

1. The problem asks for the equation of a circle given its center and a point on the circle. 2. The general equation of a circle with center $(h, k)$ and radius $r$ is:

1. The problem is to find the volume of the frustum of a cone formed by cutting a cone with a diameter of 48 cm parallel to its base. 2. First, note the total height of the origina

1. Let's state the problem: We have a triangle with two sides measuring 12cm and 15cm, and we want to find the possible range for the third side's length. 2. According to the trian

1. **Stating the problem:** We have a circle with points A, B, C, D, and E on the circumference and three triangles ABC (orange), EBD (yellow), and EAD (light yellow) inside the ci

1. We are given several geometric diagrams involving circles and angles, and we need to find the variable $z$ in each. 2. For the first diagram, angles of 48° are given at points o

1. We are given two similar triangles. The smaller triangle has base length 8 feet and height 5 feet. The larger triangle has base length 24 feet and height equal to the tree's hei

1. **State the problem:** Given triangle PQR with point S on line PR such that PSR is straight. 2. Angles PQS and SQR are on a straight line at Q, and their sizes satisfy the ratio

1. المشكلة: جد مركز الدائرة ونصف القطر. 2. لفهم مسئلة تحديد مركز الدائرة ونصف القطر، نحتاج إلى معادلة الدائرة العامّة التي تكون عادة بالصورة $$ (x - h)^2 + (y - k)^2 = r^2 $$ حيث $

1. The problem states we have two similar rectangles. One smaller rectangle has dimensions 4 cm by 7 cm. The larger rectangle has one known side length of 4.8 cm, and we need to fi

1. **State the problem:** We know a can of beans has a circular base with area 167 square inches and a height of 8 inches. We want to find the area of the label that covers the ent

1. We are given a triangle with angles 115°, 304°, and $x$.\n2. The sum of angles in any triangle is always 180°.\n3. Here, one angle is 304°, which is more than 180°, so this cann

1. **Volume of spherical ball is 4846.59 cm³, radius 10.5 cm. True or False?** Volume of sphere formula:

1. **Stating the problem:** We have triangle ABC with sides AB = BC and a point D on the extension of BA such that AB = AD. We need to find the measure of angle BCD. 2. **Understan

1. The problem states that we have a circle with radius $r = 8$ cm and a chord of length $12$ cm. 2. We need to find the distance $d$ of the chord from the center of the circle.

1. **Problem Statement:** We need to calculate the size of the interior angle labeled $c$ in a regular pentagon. 2. **Recall properties of a regular pentagon:** A regular pentagon

1. **Problem statement:** We need to find the size of angle $m$ in a quadrilateral where two pairs of opposite sides are equal, and two angles are given: $142^\circ$ and $156^\circ

1. **State the problem:** We need to find the size of an interior angle $c$ of a regular pentagon. 2. **Recall the formula for the interior angle of a regular polygon:** The measur

1. **State the problem:** We need to find the distance between points A(1, 3) and B(9, 8) using Pythagoras' theorem. 2. **Identify the coordinates:** A(1, 3), B(9, 8).

1. لنفهم السؤال، لدينا زاويتان $x$ و $51^\circ$ تقعان على خط مستقيم. 2. الزوايا المتجاورة على خط مستقيم مجموعها $180^\circ$ لأنهما يكملان الخط المستقيم.

1. Stating the problem: We are given that the measure of angle 1 ($m\angle 1$) is 55°. 2. Explanation: Based on the provided information and the description of the geometric figure