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O is the center of the circle where AD = AE. What is the

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Director
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O is the center of the circle where AD = AE. What is the [#permalink] New post 10 Apr 2007, 11:05
O is the center of the circle where AD = AE. What is the measure of the angle BOC in degrees ?

(1) The length of CO is 6.
(2) The arc BC is 2 pi long.

NOTICE: the question has been edited for errors mentioned by fellow members. Sorry
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Last edited by Mishari on 11 Apr 2007, 03:21, edited 2 times in total.
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 [#permalink] New post 10 Apr 2007, 15:03
i think there might be something wrong with the question.

in an inscribed triangle, if one side is the diameter and the opposite vertex is on the circle, that vertex should have an angle of 90. that would make the other two sides 45 degrees since the sides are isoceles.

yet in statement 1, it says that ADE is 50. i realise the figure might not be too scale, but is the assumption that the vertices of the triangle lie on the circle???
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Answer [#permalink] New post 11 Apr 2007, 09:36
Hi all

O is the center (given) and CO therefor is the circle radii R = 6 - statement (1).

The arc BC is 2 pi long (given) - statement (2).

circumference of the circle is 2Rpi = 12pi

the ratio of BC / circumference is 2 / 12

2 / 12 * 360 = 60

we can now tell that BOC = 60 degrees

so my answer is (C)

I didn't gave any weight to AD = AE - is that correct ?

:-D

Last edited by KillerSquirrel on 12 Apr 2007, 23:04, edited 2 times in total.
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Re: Geometry - Intermediate [#permalink] New post 12 Apr 2007, 07:50
Mishari wrote:
O is the center of the circle where AD = AE. What is the measure of the angle BOC in degrees ?

(1) The length of CO is 6.
(2) The arc BC is 2 pi long.

NOTICE: the question has been edited for errors mentioned by fellow members. Sorry


Arc length BC ( in degrees ) = Angle subtended in the center by the arc* (Pi/180)*radius

from here you know that we need both the statements to answer the question.

There the choice is "C".
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 [#permalink] New post 12 Apr 2007, 10:45
Correct

OA: C
  [#permalink] 12 Apr 2007, 10:45
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