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If A is the center of the circle, then which statement explains how segment EF is related to segment GF? Circle A with inscribed triangle EFG; point D is on segment EF, point H is on segment GF, segments DA and HA are congruent, and angles EDA and GHA are right angles.

A. segment EF ≅ segment GF because both segments are perpendicular to radii of circle A.

B. segment EF ≅ segment GF because both segments are the same distance from the center of circle A.

C. segment EF ≅ segment GF because the inscribed angles that create the segments are congruent.

D. segment EF ≅ segment GF because the tangents that create the segments share a common endpoint.

User Steve Boyd
by
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2 Answers

2 votes

Answer:

segment EF ≅ segment GF because both segments are the same distance from the center of circle A.

Explanation:

Hope this helps :)

User Alon Mahl
by
8.0k points
4 votes

Answer:

segment EF ≅ segment GF because both segments are the same distance from the center of circle A ⇒ answer B

Explanation:

* Lets revise some facts in the circle

- The perpendicular segment from the center of the circle to a chord

bisects it

- A segment from the center of a circle to the midpoint of a cord is

perpendicular to it

- Congruent chords in a circle are equidistant from the center of the circle,

that means the perpendicular distances from the center of the circle

to the chords are equal

- If two chords in a circle are equidistant from the center of the circle

( the perpendicular distances from the center of the circle to the

chords are equal) , then they are congruent

* Lets solve the problem

∵ ∠EDA is right angle

AD ⊥ FE

∵ ∠GHA is right angle

AH ⊥ FG

AD = AH

∵ EF and GF are chords in the circle A

∴ The chords EF and GF are equidistant from the center of the circle A

- By using the bold fact above

EF ≅ GF

* segment EF ≅ segment GF because both segments are the same

distance from the center of circle A

If A is the center of the circle, then which statement explains how segment EF is-example-1
User John Wells
by
8.0k points
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