Answer:
x = 6 , AC = [tex]\sqrt{89}[/tex]
Step-by-step explanation:
(3)
Tangents to a circle from an external point are congruent, then
4x - 9 = 15 ( add 9 to both sides )
4x = 24 ( divide both sides by 4 )
x = 6
(4)
the angle between a tangent and a radius at the point of contact is right , so
Δ ABC is a right triangle with hypotenuse AC
Using Pythagoras' identity in the right triangle
AC² = AB² + BC² = 5² + 8² = 25 + 64 = 89 ( square root both sides )
AC = [tex]\sqrt{89}[/tex] ≈ 9.4 ( to 1 dec. place )
