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HSC Stuff => HSC Maths Stuff => HSC Subjects + Help => HSC Mathematics Extension 1 => Topic started by: helkit98 on October 23, 2016, 08:24:15 pm

Title: Math Ext 1 - Cyclic Quadrilateral Q (ii)
Post by: helkit98 on October 23, 2016, 08:24:15 pm: 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.
Title: Re: Math Ext 1 - Cyclic Quadrilateral Q (ii)
Post by: jakesilove on October 23, 2016, 08:27:04 pm: Quote from: helkit98 on October 23, 2016, 08:24:15 pm
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!
Title: Re: Math Ext 1 - Cyclic Quadrilateral Q (ii)
Post by: RuiAce on October 23, 2016, 08:28:28 pm: Quote from: helkit98 on October 23, 2016, 08:24:15 pm
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.