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10 Sep 2022, 05:30
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C
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Difficulty:
55%
(hard)
Question Stats:
63% (02:25) correct
37%
(02:49)
wrong
based on 30
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If two triangles shown in the figure above are equilateral and the radius of the outer circle equals to 3, what is the radius of the smallest circle?
(A) √3
(B) 3/2
(C) 3/4
(D) 1/√3
(E) 1/(2√3)
Attachment:
2022-09-02_19-40-20.png [ 9.47 KiB | Viewed 1918 times ]
10 Sep 2022, 05:40
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Since, For an equilateral triangle, circumradius = 2 * inradius
Given circumradius = 3.. therefore, inradius of bigger equilateral triangle = \(\frac{3}{2}\)
Now this incircle acts as circumcircle of smallest equilateral triangle
therefore, the radius of the smallest circle =\(\frac{ 1}{2} * \frac{3}{2}\) (radius of circumcircle to smallest equilateral triangle)
= \(\frac{ 3}{4 }\)
Answer: C
Given circumradius = 3.. therefore, inradius of bigger equilateral triangle = \(\frac{3}{2}\)
Now this incircle acts as circumcircle of smallest equilateral triangle
therefore, the radius of the smallest circle =\(\frac{ 1}{2} * \frac{3}{2}\) (radius of circumcircle to smallest equilateral triangle)
= \(\frac{ 3}{4 }\)
Answer: C
10 Sep 2022, 08:25
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We can find the side of the triangle and the radius of the incircle in succession and arrive at the radius of the innermost (smallest circle).
Option C
Option C
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Screenshot 2022-09-10 205415.png [ 186.71 KiB | Viewed 1325 times ]
