# Circle theorems

• May 8th 2011, 03:33 AM
IBstudent
Circle theorems
This question is concerning the cyclic quadrilateral rule. My question is :
Is it possible to use the cyclic quadrilateral rule if the quadrilateral is in a semi-circle.
To make it more clear I have attached a diagram, so in the diagram, is it right to say that x+y=180 and 6q=180.

Thanks
• May 8th 2011, 03:40 AM
abhishekkgp
Quote:

Originally Posted by IBstudent
This question is concerning the cyclic quadrilateral rule. My question is :
Is it possible to use the cyclic quadrilateral rule if the quadrilateral is in a semi-circle.
To make it more clear I have attached a diagram, so in the diagram, is it right to say that x+y=180 amd 6q=180.

Thanks

yes!
• May 8th 2011, 04:07 AM
IBstudent
Quote:

Originally Posted by abhishekkgp
yes!

thanks!
• May 10th 2011, 04:50 AM
IBstudent
but what if it is the same but one angle is in the centre of the circle and the other three are touching the sides. Would the cyclic quadrilateral rule stil work?
Thanks
• May 10th 2011, 05:34 AM
I would say no.
Because for the original diagram, the quadrilateral, although in a semicircle, is also in a full circle afterall.

But when any of the four angles in not on the circumference of a full circle.

However...
There is a rule that if an angle is formed at center of circle, then it is twice the angle formed on the circumference.... both angles formed from same points.
So, for what you last asked, 0.5[angle at centre] + [opposite angle] = 180
• May 10th 2011, 02:24 PM
bjhopper
If the quadrilateral starts at the center you cannot get opposite angles to total 180 so any quad in the semicircle will not be cyclic

bjh