Question

jonathan is standing near a fountain (f) that is located at the center of a circular garden. the pizza shop (p), the book store (b), and the gift shop (g) are located as shown. which statement must be true with respect to jonathans position? a. the distance from g to p is less than the distance from f to b. b. the distance from f to g is greater than the distance from f to b. c. the distance from b to p is equal to the distance from g to p. d. the distance from f to g is equal to the distance from f to b.

Explanation:

Step1: Identify circle properties

Points $G$ and $B$ lie on the circular garden with center $F$, so $FG$ and $FB$ are radii of the circle. By definition, all radii of a single circle are equal.

Step2: Evaluate each option

• Option A: No basis to compare $GP$ and $FB$; $GP$ is a segment from a circle point to an external point, $FB$ is a radius. This is not necessarily true.
• Option B: $FG$ and $FB$ are radii, so they are equal, not greater. This is false.
• Option C: $P$ is an external point, $B$ and $G$ are distinct circle points, so $BP

eq GP$. This is false.

• Option D: $FG$ and $FB$ are radii of the same circle, so they must be equal. This is true.

Answer:

D. The distance from F to G is equal to the distance from F to B.