Question

ONLY SERIOUS ANSWERS!!!! 25 POINTS

Answer 1

FD = 25.94 or 26

Explanation:

ED = CD ...... ( Tangent secant Property)

4x + 11 = 13x - 16

11 + 16 = 13x - 4x

27 = 9x

27÷9 = x

3 = x

so,

ED = 4x + 11 = 4(3) + 11

ED = 23

FE = 12 ...... ( given )

ΔFED = 90° ...... ( tangent property )

so,

FD² = FE² + ED²

FD² = 12² + 23²

FD² = 144 + 529

FD² = 673

FD = √673

FD = 25.94

FD = 26 (approx )

Answer 2

FD≈25.94.. rounded = 26

Explanation:

FD²=12²+(4x+11)²

FD²=144+16x²+88x+121

FD²=265+16x²+88x

also

FD²=12²+(13x-16)²

FD²=144+169x²-416x+256

FD²=400+169x²-416x

thus

265+16x²+88x = 400+169x²-416x

16x²-169x²+88x+416x+265-400 = 0

-153x²+504x-135 = 0

we will solve this quadratic equation by suing the quadratic formula to find x

x=(-504±sqrt(504²-4(-153)(-135)))/2(-153)

x=(-504±
`\sqrt{504^(2)-4(-153)(-135) }`)/2(-153)

x=(-504±
`√(254016-82620 )`)/-306

x=(-504±
`√(171396)`)/-306

x=(-504±414)/-306

x=(-504+414)/-306 and x=(-504-414)/-306

x=-90/-306 and x=-918/-306

x= 5/17 , 3

substituting x by the roots we found

check for 5/17:

4x+11 = 4×(5/17)+11 = (20/17)+11 = (20+187)/17 = 207/17 ≈ 12.17..

13x-16 = 13×(5/17)-16 = (65/17)-16 = (65-272)/17 = -207/17 ≈ -12.17..

check for 3:

4x+11 = 4×3+11 = 12+11 = 23

13x-16 = 13×3-16 = 23

thus 3 is the right root

therfore

ED=23 and CD=23

FD²=FE²+ED² or FD²=FC²+CD²

FD²=12²+23²

FD²=144+529

FD²=673

FD=√673

FD≈25.94.. rounded = 26