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Re: equilateral triangle circumscribed circle [#permalink]
08 Aug 2009, 09:17
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]
08 Aug 2009, 09:30
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]
08 Aug 2009, 23:04
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]
09 Aug 2009, 00:39
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]
23 Aug 2015, 13:37
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