# Proof of a quadrilateral being cyclic

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#1

I feel like I'm missing something very obvious here, does anyone have any ideas as to how to do this?
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2 years ago
#2
Opposite angles in a cyclic quadrilateral are supplementary,and triangle ABC is isosceles. Find ACB using that hint,from there find ABC, and the answer should show up.
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#3
(Original post by ArchangelMichael)
Opposite angles in a cyclic quadrilateral are supplementary,and triangle ABC is isosceles. Find ACB using that hint,from there find ABC, and the answer should show up.
How do I reason what ABC would be?
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2 years ago
#4
(Original post by patto243)
How do I reason what ABC would be?
You've found ACB to be x,correct? The sum of angles in a triangle would be 180 degrees. Try moving from there,regardless of whether or not you get an expression as angle ABC.
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#5
(Original post by ArchangelMichael)
You've found ACB to be x,correct? The sum of angles in a triangle would be 180 degrees. Try moving from there,regardless of whether or not you get an expression as angle ABC.
Yes, apologies if I am missing your point here, however how do the angles in a triangle adding to 180 help to prove that ADC and ABC add to 180?
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2 years ago
#6
(Original post by patto243)
Yes, apologies if I am missing your point here, however how do the angles in a triangle adding to 180 help to prove that ADC and ABC add to 180?
Ok. BAC and ACB both equal x. Sum of angles in a triangle is 180 degrees. Therefore, ABC would be 180-(x+x), or 180-2x. Now, the proof of a quadrilateral being cyclic is that two opposite angles are supplementary,meaning their sum is 180 degrees. Add ABC to ADC,and you should get the answer. Sorry if I was a bit vague.
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#7
(Original post by ArchangelMichael)
Ok. BAC and ACB both equal x. Sum of angles in a triangle is 180 degrees. Therefore, ABC would be 180-(x+x), or 180-2x. Now, the proof of a quadrilateral being cyclic is that two opposite angles are supplementary,meaning their sum is 180 degrees. Add ABC to ADC,and you should get the answer. Sorry if I was a bit vague.
Thank you, that has worked.
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11 months ago
#8
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4 weeks ago
#9
Hi, did you ever find the answer?
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