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July 31st, 2013, 06:53 AM   #1
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properties of circle doubts

Given that CF is the diameter, prove that X is the centre of the circle.

How shld I prove it?
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 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. $\angle CBD= \angle CAD= 25^\circ$ because those are inscribed angles on CD. The inscribed angle on AD is $\angle ABD=180^\circ -\angle CBD - \angle PBA = 180^\circ-90^\circ=90^\circ$. 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: 7,963 Thanks: 1148 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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