April 24, 2017, 09:20:45 pm

### AuthorTopic: Math Ext 1 - Cyclic Quadrilateral Q (ii)  (Read 175 times) Tweet Share

0 Members and 1 Guest are viewing this topic.

#### helkit98

• Posts: 7
• Respect: 0
• School: vinice
##### Math Ext 1 - Cyclic Quadrilateral Q (ii)
« on: October 23, 2016, 08:24:15 pm »
0
Don't understand part ii of this question. I understand how angleCDA and angleAOC are 2x but don't get how this makes ACDO cyclic.

#### jakesilove

• ATAR Notes HSC Lecturer
• National Moderator
• Part of the furniture
• Posts: 1605
• Respect: +98
##### Re: Math Ext 1 - Cyclic Quadrilateral Q (ii)
« Reply #1 on: October 23, 2016, 08:27:04 pm »
0
Don't understand part ii of this question. I understand how angleCDA and angleAOC are 2x but don't get how this makes ACDO cyclic.

Hey! Looks like you've actually completed the proof; draw a circle around the supposed CQ, and you'll find that, based on your proof, angle subtending the same arc are equal. This will only be true for a CQ, therefore a CQ is what we have!
ATAR: 99.80

Mathematics Extension 2: 93
Physics: 93
Chemistry: 93
Modern History: 94
Mathematics: 96
Mathematics Extension 1: 98

Studying a combined Advanced Science/Law degree at UNSW

#### RuiAce

• Moderator
• ATAR Notes Legend
• Posts: 3741
• It will be ok
• Respect: +98
##### Re: Math Ext 1 - Cyclic Quadrilateral Q (ii)
« Reply #2 on: October 23, 2016, 08:28:28 pm »
0
Don't understand part ii of this question. I understand how angleCDA and angleAOC are 2x but don't get how this makes ACDO cyclic.
$\text{Theorem: If an interval subtends angles of equal size}\\ \text{and on the same size}\\ \text{then all 4 points involved are concyclic.}\\ \text{(Resulting in the quadrilateral being a cyclic one)}$
$\text{It is the converse of angles in the same segment theorem}\\ \text{aka. angles standing on same arc theorem}$
$\text{So here, }\angle CDA = \angle COA \implies C, D A, O\text{ are concylic.}$
I can let out a vent on maths in focus here. For some fucking reason it's not covered in that textbook.
Interested in Mathematics Tutoring? Message for details!

ATAR: 98.60
Currently studying: Bachelor of Actuarial Studies/Bachelor of Science (Advanced Maths) @ UNSW