Property of Circles: Segment Relationships in Circles

x = 5

Step-by-step explanation:

Two secants from an external point to a circle, then the product of one secant's external part and the entire secant is equal to the product of the external part and the entire secant of the other, that is

(x - 2)(x - 2 + x + 4) = 4(4 + 5)

(x - 2)(2x + 2) = 4(9) = 36 ← distribute and simplify the left side

2x² + 2x - 4x - 4 = 36

2x² - 2x - 4 = 36 ( subtract 36 from both sides )

2x² - 2x - 40 = 0 ( divide through by 2 )

x² - x - 20 = 0 ← in standard form

(x - 5)(x + 4) = 0 ← in factored form

Equate each factor to zero and solve for x

x - 5 = 0 ⇒ x = 5

x + 4 = 0 ⇒ x = - 4

But x > 0 ⇒ x = 5

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step-by-step explanation:

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