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Which of the following is an Inscribed angle?

Which of the following is an Inscribed angle?

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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Which of the following is an inscribed angle? 

**Question:** Which of the following is an inscribed angle? **Diagram Explanation:** The image depicts a circle with labeled points P, Q, R, and C. - **Points P, Q, and R** are located on the circumference of the circle. - **Point C** is located inside the circle. There are three line segments: 1. **Segment PQ** (in blue) connects points P and Q on the circle. 2. **Segment PR** (in purple) connects points P and R on the circle. 3. **Segment PC** (in pink) connects point P on the circle with point C inside the circle. The inscribed angle formed is ∠PQR since it is created by two chords, PQ and PR, that meet at point R on the circle's circumference. Whereas ∠PCR cannot be an inscribed angle because point C is not on the circle's circumference.
Transcribed Image Text:**Question:** Which of the following is an inscribed angle? **Diagram Explanation:** The image depicts a circle with labeled points P, Q, R, and C. - **Points P, Q, and R** are located on the circumference of the circle. - **Point C** is located inside the circle. There are three line segments: 1. **Segment PQ** (in blue) connects points P and Q on the circle. 2. **Segment PR** (in purple) connects points P and R on the circle. 3. **Segment PC** (in pink) connects point P on the circle with point C inside the circle. The inscribed angle formed is ∠PQR since it is created by two chords, PQ and PR, that meet at point R on the circle's circumference. Whereas ∠PCR cannot be an inscribed angle because point C is not on the circle's circumference.
## General Equation of a Circle The general equation for a circle is given by: \[ (x-a)^2 + (y-b)^2 = r^2 \] Where: - \((a, b)\) is the center of the circle. - \(r\) is the radius of the circle. ### Examples: 1) **Equation:** \(x^2 + y^2 = 121\) - Rearrange: \((x-0)^2 + (y-0)^2 = 11^2\) - **Center:** \((0, 0)\) - **Radius:** 11 2) **Equation:** \((x-2)^2 + y^2 = 64\) - Rearrange: \((x-2)^2 + (y-0)^2 = 8^2\) - **Center:** \((2, 0)\) - **Radius:** 8 3) **Equation:** \(\left(x+\frac{3}{2}\right)^2 + \left(y+\frac{5}{8}\right)^2 = 36\) - Rearrange: \(\left(x - \left(-\frac{3}{2}\right)\right)^2 + \left(y - \left(-\frac{5}{8}\right)\right)^2 = 6^2\) - **Center:** \(\left(-\frac{3}{2}, -\frac{5}{8}\right)\) - **Radius:** 6 4) **Equation:** \((x-1)^2 + (y+7)^2 = 9\) - Rearrange: \((x-1)^2 + (y-(-7))^2 = 3^2\) - **Center:** \((1, -7)\) - **Radius:** 3 5) **Equation:** \((x+8)^2 + (y-3)^2 = 7\) - Rearrange: \((x-(-8))^2 + (y-3)^2 = (\sqrt{7})^2\) - **Center:** \((-8, 3)\) - **Radius:** \(\sqrt{7}\)
Transcribed Image Text:## General Equation of a Circle The general equation for a circle is given by: \[ (x-a)^2 + (y-b)^2 = r^2 \] Where: - \((a, b)\) is the center of the circle. - \(r\) is the radius of the circle. ### Examples: 1) **Equation:** \(x^2 + y^2 = 121\) - Rearrange: \((x-0)^2 + (y-0)^2 = 11^2\) - **Center:** \((0, 0)\) - **Radius:** 11 2) **Equation:** \((x-2)^2 + y^2 = 64\) - Rearrange: \((x-2)^2 + (y-0)^2 = 8^2\) - **Center:** \((2, 0)\) - **Radius:** 8 3) **Equation:** \(\left(x+\frac{3}{2}\right)^2 + \left(y+\frac{5}{8}\right)^2 = 36\) - Rearrange: \(\left(x - \left(-\frac{3}{2}\right)\right)^2 + \left(y - \left(-\frac{5}{8}\right)\right)^2 = 6^2\) - **Center:** \(\left(-\frac{3}{2}, -\frac{5}{8}\right)\) - **Radius:** 6 4) **Equation:** \((x-1)^2 + (y+7)^2 = 9\) - Rearrange: \((x-1)^2 + (y-(-7))^2 = 3^2\) - **Center:** \((1, -7)\) - **Radius:** 3 5) **Equation:** \((x+8)^2 + (y-3)^2 = 7\) - Rearrange: \((x-(-8))^2 + (y-3)^2 = (\sqrt{7})^2\) - **Center:** \((-8, 3)\) - **Radius:** \(\sqrt{7}\)
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