CIRCLES 2nd Aug.

Subject: CIRCLES 2nd Aug. Sun Aug 02, 2009 11:40 pm

2 chords AB & CD intsect at P inside a circle . Prove that sum of /_s subtended by arcs AC & BD at the centre 0 = 2(/_APC).

Active member

join AD and BC

IN TRIANGLE BCP
EXT ANGLE APC = ANGLE PCB + ANGLE PBC
= ANGLE DCB + ANGLE ABC ------ i

ANGLE ABC= ANGLE ADC
ANGLE DCB = ANGLE BAD [ ANGLES IN THE SAME SEGMENT]

CENTRAL ANGLE AOC = 2 ANGLE ADC = 2 ANGLE ABC
CENTRAL ANGLE BOD = 2 ANGLE DCB

SUM OF TWO CENTRAL ANGLE =
AOC + BOD = 2 [ ANGLE ABC + ANGLE DCB ]
= 2 ANGLE APC { FROM i]
Q. E.D.