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July 31st, 2013, 06:53 AM  #1 
Member Joined: Sep 2011 Posts: 99 Thanks: 1  properties of circle doubts
Given that CF is the diameter, prove that X is the centre of the circle. How shld I prove it? 
July 31st, 2013, 11:48 AM  #2 
Senior Member Joined: Jul 2013 From: Croatia Posts: 180 Thanks: 11  Re: properties of circle doubts
We have to prove that AD is diameter of a circle. because those are inscribed angles on CD. The inscribed angle on AD is . By Thales theorem we can conclude that AD is diameter of a given circle. Diameters of a circle intersect only in center of circle, since CF is a diameter, point X is center of a circle. 
July 31st, 2013, 12:34 PM  #3 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,943 Thanks: 1132 Math Focus: Elementary mathematics and beyond  Re: properties of circle doubts
Angle ABC = 115° and quadrilateral ABCD is cyclic so angle ADC = 65°. Hence angle ACD is 90°, AD is a diameter and X is the center of the circle.


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