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Cyclic Quadrilaterals

Date: 8/30/96 at 9:27:23
From: Stephen Digby
Subject: Cyclic Quadrilaterals

A cyclic quadrilateral with angles of 120, 60, 100, 80 touches a 
circle at each vertex.  What angles do these points make with the 
centre of the circle (i.e. what size arcs do these points divide the 
circle into?

I have been thinking on this one, but can't seem to budge it!

Stephen Digby

Date: 8/30/96 at 13:50:58
From: Doctor Tom
Subject: Re: Cyclic Quadrilaterals

Any angle inscribed in a circle cuts off an arc of twice its size, so 
the arcs have sizes 240, 120, 200, and 160 degrees.

Draw a picture and draw a heavy line over the indicated arcs to 
convince yourself that they completely cover the circle twice, so a 
check of this answer should be that the angles should add to 2 times 
360 or 720 degrees.  And by golly, they do!

-Doctor Tom,  The Math Forum
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Associated Topics:
High School Conic Sections/Circles
High School Geometry
High School Triangles and Other Polygons

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