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13 Jul 2022, 08:00
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Three tangent circles are inscribed in a 60° angle, as shown above. If the radius of the blue circle is 27, what is the radius of the yellow circle ?
A. \(1\)
B. \(\sqrt[4]{27}\)
C. \(3\)
D. \(\sqrt{27}\)
E. \(9\)
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Attachment:
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13 Jul 2022, 08:12
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joining the circles from the point at 60* we see that its 30-60-90 ∆
and with each circle the distance from the point is 3 times that of the previous circle radius
so middle circle radius is 9 and yellow circle radius is 3
option C
Three tangent circles are inscribed in a 60° angle, as shown above. If the radius of the blue circle is 27, what is the radius of the yellow circle ?
A. \(1\)
B. \(\sqrt[4]{27}\)
C. \(3\)
D. \(\sqrt{27}\)
E. \(9\)
and with each circle the distance from the point is 3 times that of the previous circle radius
so middle circle radius is 9 and yellow circle radius is 3
option C
Bunuel
Three tangent circles are inscribed in a 60° angle, as shown above. If the radius of the blue circle is 27, what is the radius of the yellow circle ?
A. \(1\)
B. \(\sqrt[4]{27}\)
C. \(3\)
D. \(\sqrt{27}\)
E. \(9\)
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Attachment:
1.png
13 Jul 2022, 08:36
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Answer is C
For the blue circle, the distance from the point of the angle to the farthest point on the blue circle is 27+27+27 since the radius of the blue circle is 27. Same applies on the middle one. Radius of the middle circle should be 3*r = 27, which is 9.
And same applies on the yellow circle, 3*r=9, then we can get the radius of the yellow circle is 3.
For the blue circle, the distance from the point of the angle to the farthest point on the blue circle is 27+27+27 since the radius of the blue circle is 27. Same applies on the middle one. Radius of the middle circle should be 3*r = 27, which is 9.
And same applies on the yellow circle, 3*r=9, then we can get the radius of the yellow circle is 3.
