Asked by Mark

A)
Naveed was given a circle with the chords
and
that intersect at point
inside the circle. Ifthe length of
,
, and
, investigate this circle and find the length of segment
.
(1 point)
FG HK E
FE = 12 EG = 7 EK = 21
HE
Segment
is 25 units long.
H
E
Segment
is 19 units long.
H
E
Segment
is 84 units long.
H
E
Segment
is 4 units long.

All Answers 1

Answered by GPT-5 mini AI
By the intersecting chords theorem, when two chords intersect inside a circle the products of the segments on each chord are equal: FE · EG = HE · EK.

Given FE = 12, EG = 7, EK = 21:
HE = (FE · EG) / EK = (12 · 7) / 21 = 84 / 21 = 4.

So segment HE is 4 units long.