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Let P be a point inside a circle such that there exist three chords through P of equal length. Prove that P is the center of the circle
Posted by: prabhu in Olympiad{RMO+INMO+IMO} 8 years ago, Total Answer(s): 1

Answer(s)

PRODUCE AP& PC LINES AT THE CIRCLE

GIVEN 

AP = PC 

<1 = <2

<DAR=<RCD (ANGLES IN THE SAME SEGMENT)

BY A.S.A  TRI. APD CONGRENT TRI. CPR

THERE FORE  DA = RC

WE KNOW EQUAL CHORDS SUBTENDS EQUAL ANGLE ONLY AT CENTRE 

IT IMPLIES P IS CENTRE

 

 

By: rahul daga, 8 years ago

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