Question

Circle M has secant lines QR and UT that intersect at point S outside the circle. Find x if the measureof secant segment QS = 15, the measure of RS = 8, the measure of ST = 3x-2 and the measure of SU= 12
(1 point)
x = 10
x = 4
00:00
04:09
x = 120
x= 12

Answer 1

Use the secant-secant power theorem: (external)*(whole) are equal for both secants.

Take RS = 8 (external), QS = 15 (whole), SU = 12 (external), ST = 3x−2 (whole):

8·15 = 12·(3x − 2)
120 = 36x − 24
36x = 144
x = 4

Answer: x = 4.