This problem concerns three circles of equal radius r that intersect in a single point O...

This problem concerns three circles of equal radius r that intersect in a single point O. (See Figure 1.50.)

(a) Let W₁, W₂, and W₃ denote the centers of the three circles and let w_i = for i = 1, 2, 3. Similarly, let A, B, and C denote the remaining intersection points of the circles and set a = By numbering the centers of the circles appropriately, write a, b, and c in terms of w₁, w₂, and w₃.

(b) Show that A, B, and C lie on a circle of the same radius r as the three given circles. (Hint: The center of the circle is at the point P, where

(c) Show that O is the orthocenter of triangle ABC. (The orthocenter of a triangle is the common intersection point of the altitudes perpendicular to the edges.)