Cyclic QuadrilateralsDate: 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 Check out our web site! http://mathforum.org/dr.math/ |
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