Could someone help me pls **Mathematics Circle Problem****Problem Statement:**In the circle below, segment AB is a diameter. If the length of arc ACB is \(6\pi\), what is the length of the radius of the circle?**Diagram Description:**- A circle is depicted with a diameter labeled as segment AB.- There are points A, B, and C marked on the circumference.- Point A and Point B form the ends of the diameter.- Point C is on the circumference, forming an arc labeled ACB with a length of \(6\pi\).**Steps to Solve the Problem:**1. **Identify Relationships:** The length of arc ACB is given as \(6\pi\).2. **Use Arc Length Formula:** The arc length of a circle is given by \(L = r\theta\), where \(L\) is the arc length, \(r\) is the radius, and \(\theta\) is the central angle in radians.3. **Recognize Diameter and Central Angle:** Since segment AB is a diameter, the angle subtended by it at the center is \(180^\circ\) or \(\pi\) radians. Thus, arc ACB forms a semicircle.4. **Calculate Radius:** \[ 6\pi = r \cdot \pi \] \[ r = \frac{6\pi}{\pi} \] \[ r = 6 \] So, the length of the radius of the circle is \(6\).**Note:** The given options in the problem (numbered as 1, 2, 3, 4, 5) are not explicitly listed, but it can be inferred that the correct answer to the radius is 6.This concludes the problem and its solution explanation for students and educators.

Name: Could someone help me pls **Mathematics Circle Problem****Problem Stat
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Description: Could someone help me pls **Mathematics Circle Problem****Problem Statement:**In the circle below, segment AB is a diameter. If the length of arc ACB is \(6\pi\), what is the length of the radius of the circle?**Diagram Description:**- A circle is de

As we know the formula for arc length of circle is given by Arc length = 2πr (θ/360) where θ is…

Answered: In the circle below, segment AB is a…

Math

Geometry

In the circle below, segment AB is a diameter If the lenrth of arc ACH is 6, what is the length of the radius of the circle?

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter10: Analytic Geometry

Section10.4: Analytic Proofs

Problem 19E: Use the analytic method to decide what type of triangle is formed when the midpoints of the sides of...

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