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Major Arc..Minor Arc

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Major Arc..Minor Arc [#permalink] New post 05 Jul 2009, 14:37
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The length of minor arc AB is twice the length of minor arc BC and the length of major arc AC is three times the length of minor arc AB. What is the measure of angle BCA?

ABC is a triangle inscribed in a circle.?

Please provide me the complete slution.
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Re: Major Arc..Minor Arc [#permalink] New post 06 Jul 2009, 00:33
Minor arc BC = x
Then Minor arc AB becomes 2x (AB = twice BC)
Thus major arc AC becomes 6x (AC = three times AB)
While total arc is 360 degrees than x becomes 40; i.e.
BC=40
AB=80
AC=240
BCA angle of triangle sees the arc AB. So the angle BCA = 80/2=40 degrees ;)
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Re: Major Arc..Minor Arc [#permalink] New post 06 Jul 2009, 12:00
Doesnt the major or minor arc make any difference?? I was confused on the second statement given where it says major arc AC is equal to 3 times AB.

Then it should be like 2*pi*r - minor arc AC = 3 times minor arc AB right? I m bit confused...let me know if my thinking is wrong here.
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Re: Major Arc..Minor Arc [#permalink] New post 06 Jul 2009, 12:20
There are 3 arcs here. 2 minors and a major arc. That is the point you did not take into account.
Re: Major Arc..Minor Arc   [#permalink] 06 Jul 2009, 12:20
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