Question

I don't remember how this kind of question works. If it helps, this is module 10.04 Geometry. 98 points

Answer choices
7
20
19
6

Answer 1

• A. 7

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To solve this you need the intersecting secants theorem, which states:

• If two secant segments are drawn to a circle from an exterior point, then the product of the measures of one secant segment and its external secant segment is equal to the product of the measures of the other secant segment and its external secant segment.

Apply this to the given lengths to get:

• IK*IJ = IH*IG

Substitute values to get equation:

• (x + 2)(x + 2 + 11) = 10*(10 + 8)
• (x + 2)(x + 13) = 10*18
• x² + 15x + 26 = 180
• x² + 15x - 154 = 0

Solve the quadratic equation to get roots:

• x = 7 and x = - 22

The first root is the answer and the second root is not considered a solution as it is negative.

The matching choice is A.