Re: The circle above has radius 8, and AD is parallel
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08 Mar 2018, 00:14
Here, the chords AD and BC are parallel, angle DAC is given 45, therefore, angle BCA is also 45. Now we cant directly calculate the length of given segments, we have to apply indirect method, total circumference= seg. BXC + seg. CD + seg. DYA + seg. AB, i.e. 16pi= x+ 2x+ CD+ AB( i assumed seg BXC to be x). Now, seg CD and seg AB are equal.
Reason- mark the center of the circle, now angle of the seg AB will be twice of the angle subtended by its chord AB(45), therefore, the angle is 90. Same goes for the other one and since they have the same angle, their length of the segment will be 2*pi*r*(90/360)=16pi/4=4pi.
Therefore, 16pi=3x+4pi+4pi, this gives us x=8pi/3. Hence lenght of seg BXC is 8pi/3.