Question

Please help me I need the answer ASAP

Answer 1

d. 76

Explanation:

MK is tangent to the circle at point K and JK is radius.

`\therefore JK\perp MK\\</p><p>\therefore \angle JKM = 90°\\</p><p>\because JK \cong JN.. (Radii\: of \: same\: circle) \\</p><p>\therefore Let\: JK = JN = r\\</p><p>MJ = MN + JN = MN + r`

By Pythagorean theorem:

`JK^2 = MJ^2 - MK^2 \\</p><p>\therefore r^2 = (MN+r) ^2 - MK^2 \\</p><p>\therefore r^2 = (648+r) ^2 - (720)^2 \\</p><p>\therefore r^2 = 419,904 + 1,296 r +r^2 \\\hspace {20 pt} - 518,400\\</p><p></p><p>\therefore 0= 1,296 r - 98496\\</p><p></p><p>\therefore 1,296 r = 98496\\</p><p>\therefore r = (98496)/(1296)\\</p><p></p><p>\huge\red{\boxed {\therefore r =76\: units}}`

Hence, radius of the circle is 76 units.