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# Major Arc..Minor Arc

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Senior Manager
Joined: 26 May 2009
Posts: 305

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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.
Senior Manager
Joined: 23 Jun 2009
Posts: 361
Location: Turkey
Schools: UPenn, UMich, HKS, UCB, Chicago

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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
Senior Manager
Joined: 26 May 2009
Posts: 305

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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.
Senior Manager
Joined: 23 Jun 2009
Posts: 361
Location: Turkey
Schools: UPenn, UMich, HKS, UCB, Chicago

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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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