Intersecting Chord Theorem Proof

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I really love circle theorem proofs. Which is your favourite circle theorem?

JoelSperanzaMath
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Deserves more views and likes. Unbelievably, I am 80 y/o and just today learned about the existence of the chord chord power theorem. I am quite sure that it never came up in high school geometry or college calculus.

pauleohl
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Thank you professor for being TO THE POINT

Hillshehe
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THANK YOU. No one explained this proof to me, but it makes so much sense now. Cheers!

shadowstone
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This was an amazing explanation! Thank you for the enlightenment. 🙂

parmerapps
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Learned it has to be subtended from the same arc bc of similar triangle relationship.I didnt under stand that earlyer in highschool.

Greengales
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To what decimal place, (after 10 places the numbers change, should they?) I tested this in my CAD software and I got different numbers. A= 0.6211972 B= 0.8341628528 C= 0.2484103854 D= 2.0859821449 A*B= 0.51817962850337216 C*D= 0.51817962855212764446

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