Question

LM is tangent to the circle at N. Find the value of x.

L
N
M
(5x − 12)
0
283⁰

Answer 1

x = 10.1

Explanation:

You want the value of x in the given secant-tangent geometry.

Secant-Tangent angle

The angle between the secant ON and the tangent MN is half the measure of arc ON. The measure of arc ON is the remainder of the circle after long arc ON = 283° is subtracted:

arc ON = 360° -283° = 77°

(5x -12)° = 1/2(77°) . . . . . relation of angle to arc

10x -24 = 77 . . . . . . . . divide by °, multiply by 2

10x = 101 . . . . . . . . . . add 24

x = 10.1 . . . . . . . . . . divide by 10