Question

Secant line MA←→−
of circle G
intersects secant line TH←→
outside the circle at point P
. Point M
is between point A
and point P
. Point T
is between point H
and point P
. Determine the measure of PT¯¯¯¯¯¯¯
if PM=6
, MA=10
, and PH=24
.(1 point)
PT=

Answer 1

Use the secant-secant power theorem: (external segment)·(whole secant) is equal for both secants.

For P-M-A: PM = 6, MA = 10 → PA = PM + MA = 16, so PM·PA = 6·16 = 96.
For P-T-H: PT·PH = 96, and PH = 24, so PT = 96/24 = 4.

PT = 4.