Question 1149205: Find the radius, in cm, of the large circle if the radius of the smaller circle is 5 sqrt3 cm. The angle formed by the two radii at the center is 60 degrees.
Found 4 solutions by greenestamps, math_tutor2020, ikleyn, Edwin McCravy:
Answer by greenestamps(13200)   (Show Source):
You can put this solution on YOUR website!
The two radii, along with a chord of the large circle tangent to the small circle, form a 30-60-90 right triangle.
The hypotenuse of the triangle is the radius of the large circle; the short leg of the triangle is the radius of the small circle.
In a 30-60-90 right triangle, the length of the hypotenuse is twice the length of the short leg.
Since the length of the short leg is 5*sqrt(3) cm, the radius of the large circle is 10*sqrt(3) cm.
Answer by math_tutor2020(3817)  (Show Source):
You can put this solution on YOUR website!
There isn't enough information. A 30-60-90 right triangle will only form if the larger radius is double that of the smaller radius. However, we could easily alter the larger radius to some other value (and still meet the conditions in the instructions). Use something like GeoGebra to try out examples to see what I mean.
Answer by ikleyn(52781)  (Show Source):
You can put this solution on YOUR website! .
Wording in this problem is DEFECTIVE and does not define/ (does not describe)
the situation adequately.
There is no sense to try to improve this wording.
It is better to THROW this so called "problem" to the closest garbage bin, as it deserves it.
It does not deserve nothing else / (nothing better).
I tell it not to offend the visitor, but to explain the matter in clear form.
It is clear that the problem is picked up from outside (several years ago)
and was defective from the very beginning.
Do not spend your time for nothing trying to fix it.
Answer by Edwin McCravy(20055)  (Show Source):
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