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 C
is the center of the circle and DE
is perpendicular to FG
, then what can be determined about FH
?

(1 point)

FH=12DE


FH=CF


FH=CH+HE


FH=HG

Answer 1

FH = HG.

Reason: A diameter (DE) perpendicular to a chord (FG) bisects that chord. Therefore H is the midpoint of FG, so FH = HG.