Question

Use the image to answer the question.

A circle has a center point upper C. Points upper D, upper E, upper F and upper G lie on the circumference of the circle.

If CH=42 m
and CF=58 m
, then what is the length of FG
?

(1 point)
Responses

32 m
32 m

80 m
80 m

40 m
40 m

16 m

Answer 1

Center C to chord FG is perpendicular and bisects it, so FH = FG/2. In right triangle CFH:

(CH)^2 + (FH)^2 = (CF)^2
42^2 + (FG/2)^2 = 58^2
(FG/2)^2 = 58^2 − 42^2 = 3364 − 1764 = 1600
FG/2 = 40 → FG = 80 m.

Answer: 80 m.