Point O is the center of the circle. What is the value of X? Answer options: 24, 15, 27, 20

Accepted Solution

Answer: FIRST OPTIONStep-by-step explanation: To solve this problem you must apply the Intersecting Secant-Tangent Theorem. By definition, when a secant line and a tangent lline and a secant segment are drawn to a circle from an exterior point: [tex](Tangent\ line)^2=(Secant\ line)(External\ Secant\ line)[/tex] The total measure of the secant shown is: [tex]18+Diameter[/tex] If the radius is 7, then the diameter is: [tex]D=7*2=14[/tex] Therefore: [tex]Secant\ line=18+14=32[/tex] You also know that: [tex]External\ Secant\ line=18\\Tangent\ line=x[/tex] Keeping the above on mind, you can substitute values and solve  for x: [tex]x^{2}=32*18[/tex] [tex]x=\sqrt{576}\\x=24[/tex]