Question

(40 POINTS!!!!) find FD

Answer 1

FD= +-25.94

Explanation:

EF=CF=r(radius)=12

we know,

FD^2=EF^2+ED^2 ......(1)

and

FD^2=CF^2+CD^2 ......(2)

We Know,

area of triangle, a= 1/2xbasexHeight

a=1/2xEFxED .......(3)

and

a=1/2xCFxCD .....(4)

from equation 3 and 4

1/2xEFxED=1/2xCFxCD

=> 1/2x12xED=1/2x12xCD

=>ED=CD

=>13x-16=4x+11

13x-4x=16+11

9x=27

x=3

so

FD^2=EF^2+(ED)^2

FD^2=(12)^2+(4x3+11)^2

=>FD^2=144+529

=>FD^2=673

FD=+-25.94

Answer 2

FD = 25.94

Explanation:

13x - 16 = 4x + 11 (Tangents drawn from an external point are equal)

13x - 4x = 11 + 16

9x = 27

x = 3

substituting x in 4x + 11,

4(3) + 11

12 + 11

23

ΔFED is a right triangle,

FD² = FE² + DE²

FD² = 12² + 23²

FD² = 144 + 529

FD² = 673

FD = 25.94