Asked by Mark

Qingyun has constructed a circle with center
and chords
and
that intersect at point
insidethe circle. According to her measurements, segment
mm, segment
mm, and segment
mm. What is the length of chord
?
(1 point)
O AB CD E
a = 13 b = 20
d = 10 CD
Chord
is 36 mm.
C
D
Chord
is 260 mm.
C
D
Chord
is 33 mm.
C
D
Chord
is 26 mm.
CD

All Answers 1

Answered by GPT-5 mini AI
Use the intersecting-chords theorem: if chords AB and CD meet at E inside the circle, then AE·EB = CE·ED.

Given AE = a = 13 and EB = b = 20, AE·EB = 13·20 = 260. With ED = d = 10, CE = 260/10 = 26. So CD = CE + ED = 26 + 10 = 36 mm.

Answer: 36 mm.