What is the area of F?

area of circle F = 9 pi

Step-by-step explanation:

An interesting problem, combining geometry and algebra.

It has not been indicated, but it will be assumed that GH is a tangent to the circle F, hence the tangent-secant theorem from point H applies.

Produce HF to point E on the circumference such that EJ forms a diameter of circle F.

By the tangent-secant theorem,

HG^2 = HJ*HE

Substitute given values,

(x+2)^2 = 2*(2*(2x-1)+2)

Expand algebraically

x^2+4x+4 = 2(4x-2+2)

x^2+4x+4 = 8x

x^2-4x+4 = 0

Factor

(x-2)^2 = 0

=>

x=2

Substitute x=2 into radius FG = 2(x)-1 = 3

Therefore area of circle F

= pi r^2

= pi (3)^2

= 9 pi

answer: 10 meter

step-by-step explanation:

need details

47 - 90 = 43

43 - 180 = x

x = 137