Question

Find X in the figure below.

Answer 1

Answer:

x = 3

Explanation:

The product of the lengths of segments from the intersection point to the circle is the same for both secants.

... 1×6 = 2×x

... 6/2 = x = 3 . . . . . divide by 2

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Comment on secant geometry

Interestingly, this relation is true whether the point of intersection of the secants is inside the circle or outside.

When it is outside, the product is of the distance to the near intersection with the circle and the distance to the far intersection with the circle.