Triangle Inscribing in a Circle

Select three points at random on a unit Circle. Find the distribution of possible areas. The first point can beassigned coordinates (1, 0) without loss of generality. Call the central angles from the first point to the second andthird and . The range of can be restricted to [0, ] because of symmetry, but can range from . Then

(1)

(2)

(3)

			(4)

But

	(5)

Write (4) as

(6)

(7)

(8)

			(9)

(10)

			(11)

(12)

(13)

			(14)

• Brent-Salamin Formula
• Brent's Factorization Method
• Brent's Method
• Bretschneider's Formula
• Brianchon Point
• Brianchon's Theorem
• Brick
• Bride's Chair
• Bridge Card Game
• Bridge (Graph)
• Bridge Index
• Bridge Knot
• Bridge Number
• Bridge of Königsberg
• Brill-Noether Theorem
• Bring-Jerrard Quintic Form
• Bring Quintic Form
• Brioschi Formula
• Briot-Bouquet Equation
• Brocard Angle
• Brocard Axis
• Brocard Circle
• Brocard Diameter
• Brocard Line
• Brocard Midpoint