Fh is tangent to circle g at point f.
what is the length of the radius, r?

pythagoras theorem is given as:

as per the statement:

fh is tangent to circle g at point f.

as we know that at the point of tangency   tangent is perpendicular to radius.

in triangle gfh.

hypotenuse side = gh = 25 + r units

adjacent side = fg = r units

opposite side = fh = 35 units

using pythagoras theorem, we have;

using identity rule:

⇒

subtract from both sides we have;

subtract 625 from both sides we have;

divide both sides by 50 we have;

r = 12 units

therefore, the   length of the radius, r is, 12 units