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In the diagram below, PB is a tangent. If PA = 5, and PB - 10, find the length of AC.

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Answer:

In this diagram, we know that PB is tangent to the circle. This means that angle PAB is 90 degrees.

We also know that PA = 5 and PB = 10.

Using the Pythagorean Theorem, we can find the length of AB:

AB^2 = PA^2 + PB^2

AB^2 = 5^2 + 10^2

AB^2 = 125

AB = sqrt(125)

AB = 5sqrt(5)

Now, we can find the length of AC using the Pythagorean Theorem again:

AC^2 = AB^2 + BC^2

AC^2 = (5sqrt(5))^2 + (10)^2

AC^2 = 125 + 100

AC^2 = 225

AC = sqrt(225)

AC = 15

Therefore, the length of AC is 15.

User Jeff Stong
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