Answer :

VicMnyag

Answer:

The length of line segment AB is 12 inches for the given figure.

Step-by-step explanation:

A secant is a straight line that touches a circle twice.

As per the given figure, we have:

Secant segment  BD = (8+10) in.

External secant segment BC = 8 in.

Tangent segment = AB

When a secant segment and a tangent segment intersect at an exterior location, the square of the tangent segment's measure equals the product of the secant segment's and its external secant segment's measures.

So, AB² = BC × BD

Substitute the values in the above equation,

AB² = 8 × (8+10)

AB² = 8 × 18

AB² = 144

AB = 12

Answer:

AB = 18 cm

Step-by-step explanation:

If a tangent and a secant are drawn from an external point to a circle, then the square of the measure of the tangent is equal to the productof the measures of the secant's external part and the entire secant, that is

AB² = BC ( BC + CD ) ← substitute values

AB² = 12 ( 12 + 15) = 12 × 27 = 324 ( take square root of both sides )

[tex]\sqrt{AB^2}[/tex] = [tex]\sqrt{324}[/tex]

AB = 18 cm

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