Question

Point upper D lies on the circumference of the circle opposite to point upper E. A line segment joins upper D with upper E and passes through center point upper C. Point upper F and upper G are opposite each other on the circumference, to the left of point C. Chord upper F upper G is perpendicular to line segment upper D upper E, as indicated by a right angle marked at the point of intersection which is labeled as point upper H. A line segment joins point upper F with point upper C.

If CH=42 m
𝐶
𝐻
=
42

m
and CF=58 m
𝐶
𝐹
=
58

m
, then what is the length of FG
𝐹
𝐺
?

(1 point)
Responses

40 m
40 m

80 m
80 m

16 m
16 m

32 m
32 m

Answer 1

80 m

Reason: A radius (line through the center) perpendicular to a chord bisects the chord, so FH = sqrt(CF^2 − CH^2) = sqrt(58^2 − 42^2) = sqrt(1600) = 40 m. Thus FG = 2·40 = 80 m.