Question

Can someone give me the right answer for this please? I'm so confused

Answer 1

JK = 18

Explanation:

LK = x - 1

KJ = x + 11

LJ = LK + KJ = x - 1 + x + 11

-> LJ = 2x + 10

LM = 12

By tangent secant segment theorem:

`LK * LJ = JM^2 \\ \\ \implies \: (x - 1)(2x + 10) = {(12)}^(2) \\ \\ \implies \: x (2x + 10) - 1(2x + 10) = 144\\ \\ \implies \: 2x^(2) + 10x - 2x - 10 - 144 = 0\\ \\ \implies \: 2x^(2) + 8x - 154 = 0\\ \\ \implies \: 2(x^(2) + 4x - 77) = 0\\ \\ \implies \: x^(2) + 4x - 77 = 0\\ \\ \implies \: x^(2) + 11x - 7x- 77 = 0\\ \\ \implies \: x(x + 11) - 7(x + 11) = 0\\ \\ \implies \: (x + 11) (x - 7) = 0 \\ \\ \implies \: (x + 11) = 0 \: \: or \: \: (x - 7) = 0 \\ \\ \implies \: x = - 11 \: \: or \: \: x = 7 \\ \\ x \: can \: not \: be \: negative \\ \implies \: x \\eq \: - 11 \\ \\ \implies \: x = 7 \\ \\ \implies \: JK = x + 11 = 7 + 11 \\ \\ \implies \: \huge \: { \orange{JK =18}}`

Hope it helps you in your learning process.

Have a great day ahead.