PLEASE HELP ME IN THIS QUESTION!!!

Question

asked Dec 23, 2023 157k views

1 Answer

SnK · Answer 1 · 2023-12-27T08:40:52+0000

Answer:

CD = 16

Explanation:

Segments EF and EC are tangent and secant respectively to the circle drawn from external point E.

Thus, by tangent-secant theorem:

ED* EC= EF^2

$\implies x(x+x+7)= (15)^2$

$\implies 2x^2+7x= 225$

$\implies 2x^2+7x-225=0$

Comparing above quadratic equation with
ax^2+bx+c=0 , we find:

a = 2, b = 7, c = -225

Now, we find the value of the discriminant

$\implies b^2-4ac= (7)^2-4(2)(-225)= 1849$

Now, by quadratic formula:

$x=(-b\pm√(b^2-4ac))/(2a)$

$\implies x=(-7\pm√(1849))/(2(2))$

$\implies x=(-7\pm (43))/(4)$

$\implies x=(-7+ 43)/(4)\: or\:x=(-7- 43)/(4)$

$\implies x=(36)/(4)\: or\:x=(- 50)/(4)$

$\implies x=9\: or\:x=-12.5$

x represents length, so it can't be negative.

$\implies x\\eq -12.5$

$\implies x=9$

CD = x + 7

-> CD = 9 + 7

-> CD = 16