Please answer with method you did please fast​

LM = 8 cm

Step-by-step explanation:

LM = KN = x + 7

NM = KL = x + 7 + NQ = x + 7 + 2 = x + 9

KN×NM = 80

(x+7)(x+9) = 80

x² + 7x + 9x + 63 = 80

x² + 16x + 63 = 80

x² + 16x - 17 = 0

solution of a quadratic equation

x = (-b ± sqrt(b² - 4ac))/(2a)

a=1

b=16

c=-17

(-16 ± sqrt(256 + 4×17))/2 = (-16 ± sqrt(256+68))/2 =

= (-16 ± sqrt(324))/2 = (-16 ± 18)/2

x1 = (-16 + 18)/2 = 2/2 = 1

x2 = (-16 - 18)/2 = -34/2 = -17

x2 as negative value is no valid solution for a side length.

so, only x1 remand as solution.

=> x=1, LM = KN = 1+7 = 8, NM = KL = 1+9 = 10

d≈7.07in

step-by-step explanation:

< coa = 150 ( given)

as ba and bc are tangents

so oc and oa is perpendicular to cb and ab respectively because in circle normal passes through centre

so in quadrilateral oabc

< coa + < oab + < ocb + < abc = 360

150 +90+90 + < abc = 360

330 + < abc = 360

< abc = 360 -330 = 30

so < abc = 30

⭐dhruv⭐