Question

HELP GEOMETRY find x

Answer 1

The Power of a Point theorem tells us, if we draw a line from a certain point, no matter which line we choose, the product of the two distances from the point to the line's intersections with the circles will be constant (or, if the line is tangent to the circle, the value will be equal to the square of the distance to the point of tangency).  So,applying the tangent rule to the $x$-distance intersection and the two-intersection rule to the other, we have $x^2 = 2(2+6) = 16$, so taking the square root of the equation gives $x=4$.