Answer:
15
Step-by-step explanation:
The product of distances from P to the two intersection points along the same secant (tangent) is the same for each. For this purpose, the tangent can be considered to intersect the circle twice at the same point. That is ...
PN·PM = PQ²
x(2x +7) = (x +6)²
2x² +7x = x² +12x +36
x² -5x -36 = 0
(x -9)(x +4) = 0 . . . . . . . true for x=9, x=-4
The relevant value of x is 9.
PQ = x +6 = 9 +6
PQ = 15
