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9-Point Circle Action (Part 5)

Here's another cool property about 6 of the points of any triangle's 9-Point Circle! For previous 9-Point Circle illustrations and properties, refer to 9-Point Circle Action (Part 1) 9-Point Circle Action (Part 2) 9-Point Circle Action (Part 3A) 9-Point Circle Action (Part 3B) 9-Point Circle Action (Part 4)
Questions: 1) Which 6 points of a triangle's 9-point circle serve as vertices of these rectangles? 2) How can you formally prove what this applet informally illustrates?

Quick (Silent) Demo