cyclic quads (1 Viewer)

[Reanna]

can a cyclic quad have 3 vertices on the circumference and the other on the centre or is it then no longer a cyclic quad

 

[Tofuu]

i think all four vertices have to lie on the circumference since i don't think the rules would work out

 

[xV1P3R]

Any 3 vertices forming a triangle lie on a particular circle, so it's nothing special

 

[Jonneeh]

I dont think all 4 vertices have to be on the circumference, but if you can prove they hold the same properties as a cyclic quad, i think you can conclude it to be one?

if that made any sense

 

[khorne]

A quadrilateral is cyclic if the opposite angles sum to 180 degrees. It can still be cyclic even if the vertices do not lie on the circumference of a particular circle.

 

[Reanna]

I dont think all 4 vertices have to be on the circumference, but if you can prove they hold the same properties as a cyclic quad, i think you can conclude it to be one?

if that made any sense

thanks yeah thats what i thought but it didnt seem to sound right so thought id ask

 

[untouchablecuz]

I dont think all 4 vertices have to be on the circumference, but if you can prove they hold the same properties as a cyclic quad, i think you can conclude it to be one?

if that made any sense

you will find that if the 4th point does not lie on the circumference, then the circle will not (and cannot) exhibit properties of a cyclic quadrilateral

 

[untouchablecuz]

Just to answer this question properly:

3 points define a unique circle.

So if three of the four points lie on the circumference, then this is the ONLY circle that passes through those three points.

Since the 4th vertex does not lie on this circle, it is NOT a cyclic quadrilateral.

listen to this

 

[Drongoski]

my 2 cents

Basically a cyclic quadrilateral is one all of whose 4 vertices lie on a circle; if the vertices do not lie on a circle it is not cyclic.

Another way of saying this is: A quadrilateral is cyclic if and only if all its 4 vertices lie on a circle.

 

[untouchablecuz]

my 2 cents

Basically a cyclic quadrilateral is one all of whose 4 vertices lie on a circle; if the vertices do not lie on a circle it is not cyclic.

Another way of saying this is: A quadrilateral is cyclic if and only if all its 4 vertices lie on a circle.

yep and since 3 points define a UNIQUE circle, the 4th point of a quad must lie on this circle to be considered cyclic

 

[Drongoski]

yep and since 3 points define a UNIQUE circle, the 4th point of a quad must lie on this circle to be considered cyclic

Absolutely!