Merry Christmas from Math Man (2 Viewers)

[SpiralFlex]

I drew my diagram differently, on the first quadrant. Oh and by the way math man. What program did you use to draw that diagram. I want to know.

 

[math man]

I drew my diagram differently, on the first quadrant. Oh and by the way math man. What program did you use to draw that diagram. I want to know.

lol i used paint...i am quite the paint artist...

 

[math man]

This right?

View attachment 23984

yep that is right

 

[math man]

refer to my previous diagram

 

[IamBread]

View attachment 23985

refer to my previous diagram

The problem is, angle ABC =/= 90 degrees. It can never equal 90 degrees.

 

[IamBread]

Diagram


Working

 

[math man]

hmm..well since the question said "if they are cyclic" it works out to be 90...if you think otherwise show me your working

 

[IamBread]

Working is up there ^

Sorry about them being pictures, unfortunately it seems to be the best I can do :/

 

[math man]

where did you get angle DBC = pi/8 ...btw your approach to this question is not the best...the question said "if they are cyclic..." meaning you use circle geo to do it

 

[math man]

i saw it...dont worry...well the question only works because i said they are cyclic...even though they may not be cyclic since the question told you to assume they are you use that fact to prove it

 

[IamBread]

Triangle ODB is isosceles, with COB = pi/2, therefore OBC = pi/4. Line OA bisects angle COB, so angle AOB = pi/8. OBAC is a rhombus so diagonals cut at pi/2, using angle sum of a triangle you get angle OBC = 3pi/8.
OBC = OBD + DBC,
DBC = 3pi/8 - pi/4 = pi/8

This may not be the best method, though it does show it can't be done.

 

[IamBread]

Ah yes it did, I misread the question, I thought it asked to show that they were cyclic, then prove that thing. Seems like an odd question though.

 

[seanieg89]

Just seems a bit silly to assume something like those points being concyclic. From that assumption we can also prove things like:

-any two real numbers are equal
-triangles have angle sum 1,000,000
-any two functions are the same

 

[Carrotsticks]

Of course MathMan, it's excellent that you wish to develop your student's thinking abilities with such questions.

However, it would be nice if you verified that the question works, just to avoid future confusion and shenanigans like this =)

But please, do post more problems! We would love to attempt them!

 

[IamBread]

I agree, more problems! They be fun!

 

[math man]

well here is another complex number/circle geo question i wrote...dw this one makes no silly assumptions

 

[lydia1992]

MERRY CHRISTMAS
wish you all a good year full of successes
may God bless you

 

[Carrotsticks]

well here is another complex number/circle geo question i wrote...dw this one makes no silly assumptions

View attachment 23992

I just managed to 'prove' that Arg(z) + Arg(w) = 90 degrees. I have probably made an arithmetic error somewhere to achieve something silly like this, so I think this implies bed time.

Will be continuing this tomorrow morning.

 

[IamBread]

well here is another complex number/circle geo question i wrote...dw this one makes no silly assumptions

View attachment 23992

I shall look at that in the morning, right now I am too lazy to think

 

[math man]

I just managed to 'prove' that Arg(z) + Arg(w) = 90 degrees. I have probably made an arithmetic error somewhere to achieve something silly like this, so I think this implies bed time.

Will be continuing this tomorrow morning.

yeh that is silly..but the question only took me 10 secs to do so i dont think it is bed time just yet..yet again i did make the question