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You are not logged in. #1 20070817 07:55:19
A hard question that popped up in the exams 8years ago!...so the teacher says. #2 20070817 08:03:39
Re: A hard question that popped up in the exams 8years ago!Sh!!!!!! #5 20070817 09:32:11
Re: A hard question that popped up in the exams 8years ago!Consider the circle with centre A. The area of the sector bounded by the radii AB and AC and the arc BC (red area in diagram below) is .This is also the area of the sector bounded by the radii BA and BC and the arc CA in the circle with centre B (blue area in diagram below) and that of the sector bounded by radii CB and CA and arc AB in circle with centre C (green area in diagram below). Now add up all these areas. You get . But this actually counts the area of triangle ABC three times. So we must subtract twice the area of the equilateral triangle ABC, which is . Hence the area of the shaded region is . Last edited by JaneFairfax (20070817 10:04:23) #6 20070817 09:58:48
Re: A hard question that popped up in the exams 8years ago!I’ve made three diagrams to illustrate what I’m saying above. #7 20070817 11:44:28
Re: A hard question that popped up in the exams 8years ago!Neatly done! "The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  Leon M. Lederman #8 20140209 06:13:15
Re: A hard question that popped up in the exams 8years ago!Hi, could someone explain why the area of each is Last edited by jesjesjesjes (20140209 06:13:37) #9 20140209 07:13:34
Re: A hard question that popped up in the exams 8years ago!hi jesjesjesjes You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei 