Answer:
MN = 9.1 cm
Step-by-step explanation:
If MN is tangent of a circle then the angle M is a right angle.
We have a dimeter of acircle d = 8 cm.
Therefore the radius CM = 8 cm : 2 = 4cm.
In a right triangle CMN use the Pythagorean theorem:
[tex]CM^2+MN^2=CN^2[/tex]
Substitute CM = 4cm and CN = 9.9 cm:
[tex]4^2+MN^2=9.9^2[/tex]
[tex]16+MN^2=98.01[/tex] subtract 16 from both sides
[tex]MN^2=82.01\to MN=\sqrt{82.1}\\\\MN\approx9.1[/tex]
