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The tangent to the circle

(x + 6)^{2} + (y - 5)^{2} = 13

passes through the point $Q (5, 2) .$

Circle with tangent

Given that the tangent touches the circle at the point $P,$ find the distance from $Q$ to $P .$

Do not try to find the coordinates of $P$ . You don't need them.

Here's a diagram:

Circle with tangent and triangle

Find $| C P |$ and $| C Q |$ , then use Pythagoras. (Notice that $| C P |$ is the radius of the circle, so you can look at the equation of the circle to get that!)