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Baby Circle

A small circle fits between two touching circles so that all three circles touch each other and have a common tangent? What is the exact radius of the smallest circle?

Ab Surd Ity

Find the value of sqrt(2+sqrt3)-sqrt(2-sqrt3)and then of cuberoot(2+sqrt5)+cuberoot(2-sqrt5).

Strange Rectangle 2

Find the exact values of some trig. ratios from this rectangle in which a cyclic quadrilateral cuts off four right angled triangles.

Absurdity Again

Age 16 to 18 Challenge Level:
What is the value of the integers $a$ and $b$ where $$\sqrt{8 - 4\sqrt{3}} = \sqrt a - \sqrt b ?$$