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555-605 (Medium)|   Geometry|      
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Bunuel
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In the figure above, the circles centered at O1 and O2 have radii of 23 Jul 2020, 05:20
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In the figure above, the circles centered at \(O_1\) and \(O_2\) have radii of equal length. If \(O_1O_2=9\) and AB=3, what is the circumference of the circle centered at \(O_1\) ?

A. 6π

B. 9π

C. 12π

D. 18π

E. 36π

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C
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In the figure above, the circles centered at O1 and O2 have radii of 23 Jul 2020, 05:24
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radius of a circle = O1B or O2A
AB= 3
O1A = 3 = O2B
radius O1B = O1A+AB = 3+3 = 6
circumference = 2πr = 12π

Answer is C
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In the figure above, the circles centered at O1 and O2 have radii of 23 Jul 2020, 13:21
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How do we understand that O1O2 =9 means the distance from O1to A and from O2 to B?

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In the figure above, the circles centered at O1 and O2 have radii of 23 Jul 2020, 13:29
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How do we understand that O1O2 =9 means the distance from O1to A and from O2 to B?

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O1O2 is bifurcated into 3 equal parts O1A = AB = BO2
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In the figure above, the circles centered at O1 and O2 have radii of 23 Jul 2020, 13:30
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Oh got it!
My misunderstanding.

Thanks.

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In the figure above, the circles centered at O1 and O2 have radii of 23 Jul 2020, 15:46
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Bunuel

In the figure above, the circles centered at \(O_1\) and \(O_2\) have radii of equal length. If \(O_1O_2=9\) and AB=3, what is the circumference of the circle centered at \(O_1\) ?

A. 6π

B. 9π

C. 12π

D. 18π

E. 36π

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We know Distance between O1 and O2 is 9
Also, AB=3
Let radius of Circles Be R

From above,

Distance between O1 and O2 can be written as = (R-3) + 3 + (R-3) = 2R-3


We know 2 R-3=9
Hence, we get R=6

Circumfrance=2*pi*R= 12*pi
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In the figure above, the circles centered at O1 and O2 have radii of 26 Jul 2020, 17:04
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Bunuel

In the figure above, the circles centered at \(O_1\) and \(O_2\) have radii of equal length. If \(O_1O_2=9\) and AB=3, what is the circumference of the circle centered at \(O_1\) ?

A. 6π

B. 9π

C. 12π

D. 18π

E. 36π

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Solution:

Since O1O2 = 9 and AB = 3 and O1A = BO2, we have O1A = ½(O1O2 - AB) = ½(9 - 3) = 3. Therefore, the radius of circle O1 is O1B = O1A + AB = 3 + 3 = 6 and its circumference is 2π x 6 = 12π.

Answer: C
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In the figure above, the circles centered at O1 and O2 have radii of 13 Aug 2023, 00:15
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We can solve this problem using the following method:

Given: O1O2 = 9, AB = 3, O1B = O2A

EQ: O1B + O2A - AB = O1O2
(AB is subtracted as it is counted twice)

O1B + O2A = O1O2 + AB = 9 + 3 = 12
R + R = 12 (given)
2R = 12
R = 6

Circumference of Circle = 2πR = 2π x 6 = 12π
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