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.
In order to do so, we should first find its radius or diameter. Let's find its radius.
Radius
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.
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.
x * 2=4 * 3
Let's solve this equation for x.
Now, notice that the green segment passes through the center C of the circle. This means that its length equals the diameter. Radius is half this length.
r = x+2/2 ⇒ r = 6+2/2 = 4
Area
Now that we know the radius of the circle, we can calculate its area using the following formula.
A = π r^2
Let's substitute 4 for r to find the area.
