Question

PLEASE HELP ME IN THIS QUESTION!!! ​

Answer 1

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