In the diagram, PT is tangent to both circles. If AB = 35, PC = 30, CD = 20, what is PA?
Let PA = x.
PA · PB = PC · PD ---> x(x+ 35) = (30)(30 + 20)
x2 + 35x = 1500
x2 + 35x - 1500 = 0
(x + 60)(x - 25) = 0
x = 25
If the radius of a larger circle is increased, the ratio of AB to PA does not change!
