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 small circle is contained inside a quarter circle and tangent to one of its sides. A line segment is constructed to be tangent to the small circle and perpendicular to the other side of the quarter circle. If the line segment has length equal to 12, what is the area shaded in blue, equal to the area of the quarter circle minus the small circle?
