Answer:
16 meters
Step-by-step explanation:
[tex] In\: \odot F, \: \overline {RS} [/tex] is tangent to the circle at point R and FR is radius.
[tex] \therefore RF\perp RS[/tex] (Tangent radius theorem)
[tex] \therefore m\angle FRS = 90\degree [/tex]
So, [tex] \triangle FRS[/tex] is right angled triangle and FS is its hypotenuse.
Let FR = FT = r
FS = FT + ST = r + 9
Now, by Pythagoras theorem:
[tex]FR^2 + RS^2 = FS^2 \\ \therefore r^2 + (15)^2 = (r + 9)^2 \\ \therefore \cancel{ r^2} +225 = \cancel{ r^2} + 18r + 81\\ \therefore \: 225 = 18r + 81 \\ \therefore \: 225 - 81= 18r \\ \therefore \: 144= 18r \\ \therefore \: r = \frac{144}{18} \\ \therefore \: r =8 \: m\\ \implies \: d = 2r = 2(8) = 16 \: m[/tex]
Thus, the diameter of the fountain is 16 meters.
