Answer:
d. 76
Step-by-step explanation:
MK is tangent to the circle at point K and JK is radius.
[tex] \therefore JK\perp MK\\
\therefore \angle JKM = 90°\\
\because JK \cong JN.. (Radii\: of \: same\: circle) \\
\therefore Let\: JK = JN = r\\
MJ = MN + JN = MN + r[/tex]
By Pythagorean theorem:
[tex]JK^2 = MJ^2 - MK^2 \\
\therefore r^2 = (MN+r) ^2 - MK^2 \\
\therefore r^2 = (648+r) ^2 - (720)^2 \\
\therefore r^2 = 419,904 + 1,296 r +r^2 \\\hspace {20 pt} - 518,400\\
\therefore 0= 1,296 r - 98496\\
\therefore 1,296 r = 98496\\
\therefore r = \frac{98496}{1296}\\
\huge\red{\boxed {\therefore r =76\: units}} [/tex]
Hence, radius of the circle is 76 units.
