Whenever there are two points of intersection along a line through a point and a circle, the product of the lengths of the segments created by the point outside the circle and the points of intersection is constant for any line.
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Practice makes perfect
Often there is one or two points of intersection along a line through a point outside a circle and the circle. These points of intersection create two different segments between the point and the circle — to the first point of intersection and to the second point of intersection. In case of a tangent line, only one segment is created.
The product of the lengths of the segments created by the outer point and the points of intersection is constant for any line. In the case of a tangent line, the product of the lengths of the segments created by the outer point and the points of intersection is equal to the square of the length of the segment created by the outer point and the tangency point.
x^2=3* (9+3)
Let's solve this equation for x.
