Question

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.

Answer 1

Answer:

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

Step-by-step 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