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In the figure above, two lines are tangent to a circle at

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by AAPL » Wed May 08, 2019 6:34 am

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Manhattan Prep

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In the figure above, two lines are tangent to a circle at points \(A\) and \(B\). What is \(x\)?

1) The area of the circle is \(81\pi\).
2) The length of arc \(ADB\) is \(7\pi\).

OA C
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Source: — Data Sufficiency |

by swerve » Wed May 08, 2019 10:33 am
1) Insufficient
2) Insufficient

1+2 ) From area we can find radius \(= 9\).
From the length of arc we can find angle of \(AOB\) (\(O\) is the center of angle)
Angle = Length of arc / Circumference * 360 degrees \(\Rightarrow \frac{7\pi}{18\pi} * 360 = 140 degrees\)

Angle \(OBA = 20\) degrees
Angle \(OBC = 90\) degrees
So we can infer that angle \(ABC = 70\) degrees
Ans as triangle \(CBA\) is isosceles we can infer that \(x = 40\) degrees
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