Proof of a quadrilateral being cyclic

Watch
patto243
Badges: 2
Rep:
?
#1
Report Thread starter 2 years ago
#1
Name:  screenshot-vle.mathswatch.co.uk-2017-11-19-16-32-32-685.png
Views: 480
Size:  104.3 KB
I feel like I'm missing something very obvious here, does anyone have any ideas as to how to do this?
0
reply
ArchangelMichael
Badges: 5
Rep:
?
#2
Report 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.
0
reply
patto243
Badges: 2
Rep:
?
#3
Report Thread starter 2 years ago
#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?
0
reply
ArchangelMichael
Badges: 5
Rep:
?
#4
Report 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.
0
reply
patto243
Badges: 2
Rep:
?
#5
Report Thread starter 2 years ago
#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?
0
reply
ArchangelMichael
Badges: 5
Rep:
?
#6
Report 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.
1
reply
patto243
Badges: 2
Rep:
?
#7
Report Thread starter 2 years ago
#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.
0
reply
Mooly_Mc1
Badges: 1
Rep:
?
#8
Report 11 months ago
#8
Hi, I've read all the previous comments and I'm still not sure how to get the other two marks could some one please help.
Attached files
0
reply
chizzzzx
Badges: 1
Rep:
?
#9
Report 4 weeks ago
#9
Hi, did you ever find the answer?
0
reply
X

Quick Reply

Attached files
Write a reply...
Reply
new posts
Back
to top
Latest
My Feed

See more of what you like on
The Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

Personalise

Current uni students - are you thinking of dropping out of university?

Yes, I'm seriously considering dropping out (33)
18.86%
I'm not sure (4)
2.29%
No, I'm going to stick it out for now (57)
32.57%
I have already dropped out (3)
1.71%
I'm not a current university student (78)
44.57%

Watched Threads

View All