High School

Thank you for visiting Points E F and D are on circle C and angle G measures 60 The measure of arc EF equals the measure of arc FD. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!

Points E, F, and D are on circle C, and angle G measures 60°. The measure of arc EF equals the measure of arc FD. Circle C is shown. Line segments EC and DF are radii. Lines are drawn from points E and D to point F to form chords EF and DF. Tangents EG and DG intersect at point G outside of the circle. Angle EGD is 60 degrees, and angles GEC and GDC are right angles. The lengths of EF and DF are congruent.

Which statements about the arcs and angles are true? Select three options.

A. ∠EFD ≅ ∠EGD
B. ∠EGD ≅ ∠ECD
C. Arc ED is congruent to arc FD
D. m∠EF = 60°
E. m∠FD = 120°

Points N, P, and R all lie on circle O. Arc PR measures 120°. Circle O is shown. Line segment PN is a diameter that extends outside of the circle to point Q. Line segment OR is a radius. Lines are drawn to connect point R to points P, O, N, and Q. Lines OR and NR are congruent. The length of PO is 5 and the length of RQ is 5√3. Arc PR measures 120 degrees.

How does the measure of angle RNQ relate to the measure of arc PR?

A. Angle RNQ is equal in measure to arc PR.
B. Angle RNQ is half the measure of arc PR.
C. Angle RNQ is twice the measure of arc PR.
D. Angle RNQ is four times the measure of arc PR.

Answer :

Final answer:

In circle geometry, the properties of angles and arcs provide the answers. For the first query, ∠egd ≅ ∠ecd, arc ed is congruent to arc fd, and marc e f = 60° are true. For the second question, without more information, we can't definitively derive the relationship between the measure of arc PR and angle RNQ.

Explanation:

The questions are related to the mathematical subject of circle geometry, particularly involving arcs and angles inside a circle. Given the parameters in the questions, we can formulate three statements which are true and answer the first question:

∠egd ≅ ∠ecd: Angle EGD is congruent to angle ECD because both are inscribed angles in Circle C that intercept the same arc, ED.

arc e d is-congruent-to arc f d: Given that EF and FD are congruent chords in the circle, the arcs they intercept are also congruent, hence arc ED is congruent to arc FD. marc e f = 60°: Since angle EGD is 60 degrees, the intercepted arc EF is also 60 degrees. This is based on the property that the measure of an inscribed angle in a circle is half the measure of its intercepted arc.

For the second question, the comparison is between the measure of angle RNQ and the measure of arc PR. In a circle, the measure of an angle formed by two chords (here RN and NQ) is half the sum of the measures of the arcs intercepted by the angle and its vertical angle (here arcs PR and NO). Given we only have the measure for arc PR (120 degrees), we cannot definitively determine the relationship between the measure of arc PR and angle RNQ without more information.

Learn more about Circle Geometry here:

https://brainly.com/question/27802544

#SPJ11

Thank you for reading the article Points E F and D are on circle C and angle G measures 60 The measure of arc EF equals the measure of arc FD. We hope the information provided is useful and helps you understand this topic better. Feel free to explore more helpful content on our website!

Rewritten by : Jeany

Other Questions