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02 Sep 2009
Iii unlike points A, B and C lie on the circumference of a circle
02 January 2022, 03:35
Iii different points A, B and C lie on the circumference of a circle. Is bespeak O the middle of the circle?
(1) AO = BO
(2) CO = BO
Dream Score Representative
07 Oct 2021
Re: Three different points A, B and C lie on the circumference of a circumvolve
04 Jan 2022, 13:11
3 unlike points A, B and C lie on the circumference of a circle. Is point O the center of the circle?
(one) AO = BO
(2) CO = BO
Argument 1 Alone:
O tin be the midpoint of any chord AB, so O does not have to be the heart of the circle. Thus statement one alone is bereft.
Statement 2 Lone:
Like to argument 1, statement two lone is insufficient.
Both Statements Combined:
We take \(AO = BO = CO\). Presume point O is not the center of the circle. Then we can try drawing a new circle with point O as the center. Yous will find that no matter what circumvolve y’all depict, you can only find 2 points of contact at most with the original circumvolve. Thus O must be the center of the original circumvolve. Combined this is sufficient.
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Re: Three unlike points A, B and C prevarication on the circumference of a circle [#permalink]
04 Jan 2022, 13:11
DS Forum Moderator
Points O a B Lie on a Line
Originally posted 2022-08-03 17:09:32.