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The four new line segments are equal because they are all radii of the two circles (with the same radius!) Now to show that ¯¯¯¯¯¯¯¯¯CD is a perpendicular.

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A perpendicular bisector is a line or line segment that intersects a given line segment at a 90°90° angle and passes through the given segment's midpoint, thus dividing the line .