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19 Mar 2021, 02:30
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
85%
(hard)
Question Stats:
43% (02:21) correct
57%
(02:14)
wrong
based on 37
sessions
History
Date
Time
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Not Attempted Yet
A quarter circle with radius 4 cm has a circle inscribed in it as shown above. What is the diameter of the inscribed circle ?
A. \(\frac{3}{1+\sqrt{2}}\)
B. \(\frac{4}{1+\sqrt{2}}\)
C. \(\frac{5}{1+\sqrt{2}}\)
D. \(\frac{6}{1+\sqrt{2}}\)
E. \(\frac{8}{1+\sqrt{2}}\)
Attachment:
1045966_f946153db51a405bb0a4234ae0109dc2.png [ 4.42 KiB | Viewed 4020 times ]
19 Mar 2021, 02:51
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From B draw an extension passing through the center of inscribed circle and touching the arc of the quarter.
Say center of the inscribed circle is O and extended line touches arc at D
BD= 4
BO+OD=4
Radius of the inscribed circle is r
r(1+\sqrt{}2)=4
r=4/(1+\sqrt{}2)
Correct answer is B
Say center of the inscribed circle is O and extended line touches arc at D
BD= 4
BO+OD=4
Radius of the inscribed circle is r
r(1+\sqrt{}2)=4
r=4/(1+\sqrt{}2)
Correct answer is B
20 Mar 2021, 17:31
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Bunuel
The radius of the big circle is consisted of two segments OA and AB. Let AB = x, then \(OA = \sqrt{2}*x\) and \(AB = x\).
Then OB = \(\sqrt{2}x + x = 4\)
\(x = \frac{4}{\sqrt{2} + 1}\) however the question is asking for diameter which is 2x.
Ans: E
Attachments
circleInCircle.png [ 28.35 KiB | Viewed 3599 times ]
