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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
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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.
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July 31st, 2013, 12:34 PM   #3
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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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