Double-click on the movie to PLAY.

Click once to PAUSE.

RELOAD the page to return to the START of the movie.

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Another method:

Triangle MPA is rotated through 90˚, with P mapped to Q.

It turns out that AQA' is a straight line (though it may not quite look it!).
Why?

The resulting triangle MAA' is isosceles and right-angled.

Therefore angle MAQ = 45˚ and so the red line bisects the angle at A.