Three squares are constructed on the three sides of an equilateral triangle. Each square has a side length equal to 1. A circle circumscribes the squares, as shown. What is the radius of the circle?
In a circle of radius 1, an equilateral triangle is inscribed in the circle as shown. What is the area of the blue region?
A square has a side length of 7. On each corner, a quarter circle with radius 3 is constructed with the corner as its center. And on the midpoint of each side, a semicircle with radius 2 is constructed with the midpoint as its center. What is the difference between the orange shaded areas and the blue shaded areas?
Triangle ABC has sides AB = 8, BC = 7, and AC = 9. The segments AB and AC are extended and a circle O is constructed exterior to the triangle and is tangent to BC at D and the extended lines through AC and AB at N and M, as shown. What is the radius of circle O?
Let ABC be the triangle with AB = 1, AC = 3, and ∠BAC = π/2. If a circle of radius r > 0 touches the sides AB, AC and also touches internally the circumcircle of the triangle ABC, then the value of r is ___.
A circle contains 4 identical squares, as shown below. If each square has a side length equal to 2, what is the radius of the circle?
