For a given point and a circle, the product of the lengths of the two segments from the point to the circle is constant along any line through the point and circle.
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Practice makes perfect
Let's begin with recalling that for a given point and a circle, the product of the lengths of the two segments from the point to the circle is constant along any line through the point and circle. Now, consider the given diagram.
In our diagram, the point which will follow this rule is the point of intersection of the shown chord segments. Therefore, the products of the lengths of the chord segments are equal.
