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Re: equilateral triangle circumscribed circle [#permalink]

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08 Aug 2009, 10:17

yezz wrote:

crejoc wrote:

In the figure (attached), ABC is an equilateral triangle, and DAB is a right triangle. What is the area of the circumscribed circle?

(1) DA = 4 (2) Angle ABD = 30 degrees

FROM STEM : DB = DIAMETER

from 1

da = 4 , , db bisects cba,we can know angles of the right triangle and thus the hyp = diam and thus we can get the radius...suff

from 2 we dont have any side length...insuff

A

I could not get where the stem says DB is the diameter?? For me it is C. We need to find the length of a side of equilateral triangle in order to find the radius and hence the area of the circle.

Re: equilateral triangle circumscribed circle [#permalink]

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08 Aug 2009, 10:30

Economist wrote:

yezz wrote:

crejoc wrote:

In the figure (attached), ABC is an equilateral triangle, and DAB is a right triangle. What is the area of the circumscribed circle?

(1) DA = 4 (2) Angle ABD = 30 degrees

FROM STEM : DB = DIAMETER

from 1

da = 4 , , db bisects cba,we can know angles of the right triangle and thus the hyp = diam and thus we can get the radius...suff

from 2 we dont have any side length...insuff

A

I could not get where the stem says DB is the diameter?? For me it is C. We need to find the length of a side of equilateral triangle in order to find the radius and hence the area of the circle.

Combining 1 and 2 we can get the length of AB.

try to draw any right angle triangle with 3 verticies on the circle and the right angle is one of these verticies without the hyp being the diameter!

Re: equilateral triangle circumscribed circle [#permalink]

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09 Aug 2009, 00:04

crejoc wrote:

yezz wrote:

db bisects cba,we can know angles of the right triangle

How can we Know the angles of the right triangle, can you explain that..

any equilateral triangle drawn inside a circle (60,60,60 angles) and if you draw the diameter it will bisect one side and one angle.ie: the triangle is exactly in the middle of the circle and the diameter cut it into halves ( similar triangles).

if we draw the 3 perpendicular bisectors of the triangle's 3 angles they will intersect at the center of the circle.

Re: equilateral triangle circumscribed circle [#permalink]

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09 Aug 2009, 01:39

yezz wrote:

crejoc wrote:

yezz wrote:

db bisects cba,we can know angles of the right triangle

How can we Know the angles of the right triangle, can you explain that..

any equilateral triangle drawn inside a circle (60,60,60 angles) and if you draw the diameter it will bisect one side and one angle.ie: the triangle is exactly in the middle of the circle and the diameter cut it into halves ( similar triangles).

if we draw the 3 perpendicular bisectors of the triangle's 3 angles they will intersect at the center of the circle.

Got it, that was really nice .. thanks for letting know it..

Re: In the figure (attached), ABC is an equilateral triangle, [#permalink]

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23 Aug 2015, 14:37

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