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 FC=20 m
𝐹
𝐶
=
20

m
and FH=12 m
𝐹
𝐻
=
12

m
, what is the length of HE
𝐻
𝐸
?

(1 point)
Responses

4 m
4 m

16 m
16 m

6 m
6 m

8 m

Answer 1

FC is the radius, so CE = 20. The perpendicular from the center to a chord bisects the chord, so CH = sqrt(FC^2 − FH^2) = sqrt(20^2 − 12^2) = sqrt(400 − 144) = 16. Thus HE = CE − CH = 20 − 16 = 4 m.

Answer: 4 m.