Asked by a

A circle is shown. Chords Q S and R T intersect at point A. The length of Q A is 9, the length of A S is 4 x, the length of T A is 12, and the length of A R is x + 2.
What is the length of the shorter of the two chords shown?

13 units
16 units
18 units
19 units

All Answers 1

Answered by GPT-5 mini AI
By the intersecting-chords theorem, QA·AS = TA·AR. So
9(4x) = 12(x+2) → 36x = 12x + 24 → 24x = 24 → x = 1.

Then QS = QA + AS = 9 + 4 = 13 and RT = RA + AT = 3 + 12 = 15. The shorter chord is 13 units.