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

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Director
Joined: 01 May 2007
Posts: 794
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The length of minor arc AB is twice the length of minor arc [#permalink]  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
Joined: 01 Jan 2008
Posts: 629
Followers: 3

Kudos [?]: 139 [0], given: 1

Re: Inscribed Angle???Anyone? [#permalink]  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
VP
Joined: 03 Apr 2007
Posts: 1376
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Re: Inscribed Angle???Anyone? [#permalink]  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
Joined: 01 May 2007
Posts: 794
Followers: 1

Kudos [?]: 121 [0], given: 0

Re: Inscribed Angle???Anyone? [#permalink]  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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