A Triangle and Two Circles

A circle of radius R is circumscribed around an isosceles triangle of height h and base b. The triangle is circumscribed around a unit circle (radius = 1).
  1. Find b in terms of h.
  2. Find R in terms of h. If h=4, find R.
  3. Find h such that the base of the triangle is the diameter of the large circle (b=2R).
  4. Find h in terms of R. If R=4, find h.
An isosceles triangle has two sides equal in length, with the third side called the "base"; for this problem, the height is measured perpendicular to the base. To be circumscribed means that each circle touches the triangle in three places.

Source: Original.

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