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?

Find the smallest integer solution to the equation 1/x^2 + 1/y^2 = 1/z^2

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

If the last four digits of my phone number are placed in front of the remaining three you get one more than twice my number! What is it?

Four rods are hinged at their ends to form a quadrilateral with fixed side lengths. Show that the quadrilateral has a maximum area when it is cyclic.

If x + y = -1 find the largest value of xy by coordinate geometry, by calculus and by algebra.