Proving Something ... (1 Viewer)

[Dreamerish*~]

If two circles touch each other, show that the line joining their centres passes through their point of contact.

How do you prove that? I thought it was just a rule we needed to know. I know how to explain it in a lot of words, but there's probably a shorter way.

 

[Pace_T]

hmmphh i can put it in words as well but im guessing
the two circles touch, therefore they have the same tangent at that point
a tangent to the radius is 90degrees
hence the sum of both of the angles formed is 180degrees
hence it is a st. line on the point
.'. the line passes thru the point
haha i think i am making it up lol
i dunno lol

 

[Dreamerish*~]

hmmphh i can put it in words as well but im guessing
the two circles touch, therefore they have the same tangent at that point
a tangent to the radius is 90degrees
hence the sum of both of the angles formed is 180degrees
hence it is a st. line on the point
.'. the line passes thru the point
haha i think i am making it up lol
i dunno lol

LOL yeah, I was just playing around with those things. I can never be 100% sure whether I really proved it or not. I know that the statement is true, it's so annoying.

 

[Templar]

That's a perfectly valid proof.

 

[ioniser]

yep thats perfectly right


but dam i hate those cicle questions hahahhahahahhah moreover those harder 3 u circle questions in 4 u

 

[klaw]

yeah circle geo sucks

 

[+Po1ntDeXt3r+]

its a euclidean proposition...
http://aleph0.clarku.edu/~djoyce/java/elements/bookIII/propIII12.html

to find it.. use the 2/3U syllabus' correct wording hope tat helps..

 

[tempco]

its a euclidean proposition...
http://aleph0.clarku.edu/~djoyce/java/elements/bookIII/propIII12.html

to find it.. use the 2/3U syllabus' correct wording hope tat helps..

whoa, don't you med students have body parts to memorise? or do you still have time to help out 3u students?

 

[+Po1ntDeXt3r+]

haha i loved maths.. i dun get to do it enough..
noi did the body part thing..
i should be exam revising for my clinical exams.. but cant i help in 3u ..?

 

[Slidey]

Re tangnet to circle: as a proof that the normal to the tangent at the point of contact passes through the centre of the circle, is it valid to construct a right angle with the normal as the hypotenuse, then apply alternate segment theorem? Or would you have to then prove alternate segment theorem?

 

[+Po1ntDeXt3r+]

from a High school Point of view.. :

Let this be ure */ insert religious text of choice /*: http://www.boardofstudies.nsw.edu.au/syllabus_hsc/pdf_doc/maths23u_syl.pdf

see part 2.9 (page 26)
technically u cant to prove dreamerish's q .. cos ure expected to use other axioms from part 2.8 or 2.3..

 

[insert-username]

Re tangnet to circle: as a proof that the normal to the tangent at the point of contact passes through the centre of the circle, is it valid to construct a right angle with the normal as the hypotenuse, then apply alternate segment theorem? Or would you have to then prove alternate segment theorem?

Isn't it one of the "laws" of circle geometry that the radius of a circle drawn at point of contact to a tangent is perpendicular to the tangent? Therefore, the normal to the tangent, which is also perpendicular to it, by definition passes through the centre of the circle because it is the radius drawn at point of contact. Shouldn't that work?


I_F

 

[Templar]

I don't think it's an axiom that a tangent must be normal to the radius, since it can be proved using contradiction.

 

[Dumsum]

I was always taught it like this: you have the radius bisecting chord at right angle property, right? That can be shown easily enough using congruent triangles. Now make the chord smaller and smaller until the chord 'becomes' a tangent... it would still be cutting at 90°.