Angle in a Semicircle (4 of 6: Coordinate geometry proof)

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  1. Eddie Woo
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Thank u so much. This is the first time i have understood this formula

heloo
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For those who may worry that there may be cases of division by 0 (x-x1) = 0 or (x-x2) = 0

You can bypass the m1m2= -1 by not considering gradients but rather dot product of vectors PA and PB

namely vector PA = <x1 - x, y1 - y>
vector PB = <x2 - x, y2 - y>

Dot product is (x1 - x)(x2 - x) + (y1 - y)(y2 - y) = 0
With some rearrangement and algebraic manipulation is equivalent to the statement
(y - y1)(y - y2) = -(x - x1)(x - x2) obtained from m1m2= -1

沈博智-xy
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Big fan of you Sir. Inspired by you I have also opened my youtube channel. I don't know if it will work or not but you inspire me to do the hardwork and just don't think about the result ❤

powerfulmath