00:01
Okay, this is problem number 18.
00:04
They tell us that pt is tangent to the circle, and they want us to find the length that's indicated.
00:13
And what they're telling us, then, they're giving us that pt is a length of 12.
00:22
A cd has a length of 18, and they're asking us to find the length of pc.
00:31
Okay, so we know that pc is going to equal to cd plus pd, okay? which also means if we turn this around, that the pd will equal pc minus the 18.
01:07
So let's make sure and set p .c equal to x.
01:15
So then pd is going to equal x minus 18.
01:22
We know then that when a sequence segment and a tangent segment are drawn to a circle from the same external point of p, that the product of the sequence segment and its external segment, it's going to equal the square of the tangent segment.
01:39
So what that says is pt is squared is going to be the same thing as pd times pc.
01:55
So if we substitute in, we know pt is 12 squared.
02:01
Pd we said is x minus 18 and pc as x.
02:09
So we have 144 is equal to x squared.
02:15
Minus 18.
02:21
Okay, let's move the 144 to the other side...