📐 geometry

1. **State the problem:** We are asked to determine whether the measure of an intercepted arc of an inscribed angle is one half the measure of the inscribed angle. 2. **Recall the

1. Statement of problem: Find the radius, diameter, center, and other circle parts as labeled, then solve algebraic problems involving central and inscribed angles. 2. Definitions:

1. Stating the problem: We need to find the total surface area enclosing the region common to the three cylinders given by $$x^2 + y^2 = 3^2, \quad x^2 + z^2 = 3^2, \quad z^2 + y^2

1. Problem: Find the image of point A(−1, 3) after reflection about the line $x=4$ followed by reflection about the Y-axis. Step 1: Reflect A about $x=4$. The formula for reflectio

1. We are given a triangle ABC with vertex C at the top and an isosceles triangle where sides AC and BC are equal. 2. The measure of angle m(AB) is given as $\frac{1}{4}$ of the le

**Exercice 1 :** Soit ABC un triangle, et D un point tel que $\vec{AD} = \vec{AB} - \vec{AC}$.

1. **Problem statement:** We have an isosceles triangle ABC with sides AB = AC, angle $A = 48^\circ$, and a circle inscribed in the triangle. The circle's radius (inradius) is 11 c

1. The problem is to understand what transformations in geometry are and explore the common types. 2. Geometric transformations change the position, size, or shape of figures in a

1. The task "connect with dots" is ambiguous in a mathematical context. 2. If you mean connecting points (dots) on a coordinate plane, this usually involves plotting points and dra

1. The problem asks us to find the angle $x$ in degrees for the sector labeled $x$ in a pie chart. 2. Pie charts represent parts of a whole, and the whole circle measures 360 degre

1. Let's analyze the first graph (top-right): Triangle ABC is inscribed in a circle with center O. - Given: Angle at C is $60^\circ$.

1. **State the problem:** We have a trapezoidal shape with a top length of 22 mm and a right side length of 11 mm. The shading is on the two upper triangular regions adjacent to th

1. Stating the problem: We need to find the area of a square whose one side length is 100 cm, and express the area in square meters. 2. Convert the side length from centimeters to

1. The problem states that one side of a square measures 100 cm. 2. Recall that all sides of a square are equal in length.

5. Given $m\angle GC = 149^\circ$ and $m\angle LSC = 39^\circ$, with $OK$ tangent to circle $C$, to find $m\angle C$ we would use properties of tangents and angles subtended by cho

1. The problem is to find the equation of a circle given its center and a point on the circle. 2. The center of the circle is given as $ (4, 3) $.

1. **State the problem:** We have a circle with diameters \(\overline{AC}\) and \(\overline{BD}\) intersecting at center \(P\). The arcs \(BC\) and \(AD\) have measures \((4k + 159

1. We are given a circle with center at $(-9.3, 4.1)$ and radius $\sqrt{13}$. 2. The general equation of a circle with center $(h,k)$ and radius $r$ is

1. Stating the problem: We are given a circle with center at $(-9.3, 4.1)$ and radius $\sqrt{13}$. We need to write the equation of this circle. 2. Recall the standard form of the

1. **Find the unknown sizes of angles (2 diagrams):** - Diagram 1: Two lines intersecting with angles $2x^\circ$, $x^\circ$, and $y^\circ$.

1. The problem involves constructing a circle with center E, diameter DW, radius EL, and examining angles and arcs related to these points. 2. We start by drawing circle with cente