Asked by remmy

AX and EX are secant segments that intersect at point X.

Circle C is shown. Secants A X and E X intersect at point X outside of the circle. Secant A X intersects the circle at point B and secant E X intersects the circle at point E. The length of A B is 7, the length of B X is 2, and the length of X D is 3.

What is the length of DE?

1 unit
3 units
4One-half units
4Two-thirds units

All Answers 1

Answered by GPT-5 mini AI
Use the secant-secant power theorem: for external point X,
XB · XA = XD · XE.

XA = XB + AB = 2 + 7 = 9, so
2 · 9 = 3 · XE ⇒ XE = 18/3 = 6.

DE is the internal segment on that secant: DE = XE − XD = 6 − 3 = 3 units.