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The length of minor arc AB is twice the length of minor arc

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Director
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The length of minor arc AB is twice the length of minor arc [#permalink] New post 07 Jul 2008, 16:16
The length of minor arc AB is twice the length of minor arc BC and the length of minor arc AC is three times the length of minor arc AB. What is the measure of angle BCA?

Picture a Triangle inscribed in a circle. Each point touching the circle is A, B, C..

20
40
60
80
120

Can anyone help explain?
Director
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Re: Inscribed Angle???Anyone? [#permalink] New post 07 Jul 2008, 16:21
jimmyjamesdonkey wrote:
The length of minor arc AB is twice the length of minor arc BC and the length of minor arc AC is three times the length of minor arc AB. What is the measure of angle BCA?

Picture a Triangle inscribed in a circle. Each point touching the circle is A, B, C..

20
40
60
80
120

Can anyone help explain?


BC = x, AB = 2x, AC = 6x -> angle BOA = 2x*(360/9x)=80 -> BCA = (1/2)*BOA = 40 -> B
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Re: Inscribed Angle???Anyone? [#permalink] New post 07 Jul 2008, 16:46
jimmyjamesdonkey wrote:
The length of minor arc AB is twice the length of minor arc BC and the length of minor arc AC is three times the length of minor arc AB. What is the measure of angle BCA?

Picture a Triangle inscribed in a circle. Each point touching the circle is A, B, C..

20
40
60
80
120

Can anyone help explain?



The angle formed at the center by the minor arc = 2 * Interior angle formed by the minor arc

let b be the length of minor arc BC

length of minor arc AB = 2b
length of minor arc AC =6b

The angle formed at the center by the minor arc = (2b/9b)*360 = 80

Interior angle formed by the minor arc = 40
Director
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Re: Inscribed Angle???Anyone? [#permalink] New post 07 Jul 2008, 16:58
Yeah, it is B. I botched this because I forgot to take x times 2....
Re: Inscribed Angle???Anyone?   [#permalink] 07 Jul 2008, 16:58
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The length of minor arc AB is twice the length of minor arc

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