Find the value of x . Two segments starting from a point outside the circle intersect the circle at two points that divide the segments. In first segment, the length of the segment inside the circle is 7 units and the segment outside the circle is 5 units. In second segment, the length of segment inside the circle is 4 units and the segment outside the circle is labeled x. x =

If two secants are drawn frm an external point to a circle, then the product of the measures of one secant's external part (outside) and that entire secant is equal to the product of the measures of the other secant's external part and that entire secant, that is

x(x + 4) = 5(5 + 7) = 5 × 12 = 60

x² + 4x = 60 ( subtract 60 from both sides )

x² + 4x - 60 = 0 ← in standard form

(x + 10)(x - 6) = 0 ← in factored form

equate each factor to zero and solve for x

x + 10 = 0 ⇒ x = - 10

x - 6 = 0 ⇒ x = 6

However, x > 0 , then x = 6