The following figure shows an equilateral triangle

Chapter 9, Problem 53

(choose chapter or problem)

The following figure shows an equilateral triangle inscribed in the unit circle. (a) Specify polar coordinates for the points A, B, and C. (b) In the figure, P denotes an arbitrary point between the origin and A on the x-axis. Let the polar coordinates of P be (r, 0). Use the distance formula for polar coordinates to show that (PA)(PB)(PC) 1 r3 [This result is due to the English mathematician Roger Cotes (16821716).]

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