3530.11 – Diameter of a Circle

Two frogs are sitting around a perfectly circular pond. Zinc, a green frog, emits the sound of a loose banjo string, and Kitty, a spring peeper, goes “boo-beep!” Let FR be the diameter of the pond, as in the figure below. Tangents FG and RS are drawn, so that segments FS and RG intersect on a point on the circle. If FG = f and RS = r, with f ≠\neq r, then the diameter FR of the pond is:

  1. ∣f−r∣|f-r|
  2. f+42\frac{f+4}{2}
  3. fr\sqrt{fr}
  4. frf+r\frac{fr}{f+r}
  5. fr2(f+r\frac{fr}{2(f+r}

3530_11_7d4410f1b5.png

Solution