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 SAWAAL JAWAAB

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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} 3 months ago, Total Answer(s): 1

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, 3 months ago

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