I subscribed for blackpenredpen, not for blackpenredpenbluepen. I am very dissapointed.
alitrux
My Number Theory professor disagreed with the theorem after I told him what it was. LOL
chesteezy
night before maths exam. this man is amazing
Klayx_
Stuff from the 8:40 point is unnessecary. Angle AOB equals (180-2y+2x) from AOB triangle. Angle COB equals (180-2y) from COB triangle. Angle AOC equals angle AOB minus angle COB and that's (180-2y+2x)-(180-2y)=180-2y+2x-180+2y=2x, Q.E.D.
HWMREWesker
We can use it for writing equation of angle bisector but it will be a little bit longer than comparing distances of point from both rays of angle
holyshit
Precisely my thinking, I like to show precisely these three variations. Thank you for the video.
ankaparnahajova
The proof I like most is the one that starts with A&B on opposite sides of a diameter. Once you prove that, you can prove the other two cases you have quickly.
ingiford
What is the integral of sqroot(sinx) from 0 to pi?
I found it 2√(2/π)(gamma(3/4))^2 in wolfram alpha which seems very interesting.can you provide me the magical steps?
debrajbanerjee
Why are you keep this name blackpenredpen
MA-mpmx
Picking a point on the minor arc AC is still good. In which case, the central angle AOC is a "reflex angle", and the inscribed angle ABC is an obtuse angle and is half of the reflex angle AOC.
qqqquito
The day blackpenredpen did simple things.
thetophatgentleman
You forgot the prove the case when the segment AB colinear to the segment AO!!
gnikola
our school requires us to write angle at centre twice angle at circumference
yaleng
Instead of saying that taking a point in the minor arc would be no good, you could have just stated why. It's a basic explanation and you just subtract both angles by 360°.
Btw I had this in my curriculum 5 years ago and I still haven't forgotten this beautiful theorem wow good job bprp
akshat
Yay...I just learned a new trick..Thanks BPRP
UnathiGX
I use central angle theorem for construction regular 2n gon after construction n gon with given side length
holyshit
crap, this is obvious -.-
I feel embarrassed now
AndDiracisHisProphet
I think until 5:45 was the essential part of the proof, since if we join A and C we get a chord AC of a circle and angles subtended by a chord of a circle on it are all equal. But I really like that you did the other case as well for completeness :)
teekayanirudh
If I squint my eyes and tilt my head, your diagram kinda looks like a pentagram.
Generalth
Now it makes sense how Thales thm works, cause the diameter's central angle is 180 degrees.
