Find the Angle
Refer to the figure below. A circle of radius 1 is tangent to a circle of radius 3. The segment OA passes through the centers of the circles. The segment OB is tangent to both circles. Find the degree measurement of the angle AOB.
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Solution to Find the Angle
Correct solutions were submitted by: Yunxi Wei, Wyatt Witemeyer, Bethany Witemeyer
In the figure below, the length of the segment from D to F is 1 and the length of the segment from E to G is 3. If the distance from O to D is x then the distance from O to E is x+4. From similar triangles we see that x is to 1 as x+4 is to 3. Solving this equation gives x = 2. Therefore the sine of the angle in question is 1/2, making the angle itself have 30 degrees.
