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=33 cm
𝐹
𝐶
=
33

cm
and CH=13 cm
𝐶
𝐻
=
13

cm
, then what is the length of FH
𝐹
𝐻
to the nearest centimeter?

(1 point)
cm

Answer 1

Since DE is a diameter and FG is perpendicular to DE at H, H is the midpoint of chord FG, so CH is the distance from the center to the chord. Thus FH = sqrt(FC^2 − CH^2) = sqrt(33^2 − 13^2) = sqrt(920) ≈ 30.33 cm.

To the nearest centimeter: 30 cm.