CATPREP 3 - geometry
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Source: Beat The GMAT — Data Sufficiency |
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DanaJ
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This problem requires some knowledge about inscribed angles in a circle.
1. notice that angle AOB and angle ACB subtend the same minor arc: AB. Since this is the case, then ACB's measurement is a piece of cake (provided you know the theorem, of course). ACB will be 2 times smaller than AOB, since ACB has its vertex on the circle and AOB has its vertex in the origin. This makes ACB 75 degrees.
2. Again, we use the property outlined above, except that in this case we need to find out the measurement of AOB.
AOB subtends minor arc AB of 10pi/3. The total length of the circle is 2Pi*radius = 2*4*Pi = 8Pi and corresponds to the whole circle of 360 degrees. You get:
8Pi...............360 degrees
10Pi/3...........x degrees
x will be [(10Pi/3)*360]/8Pi = 150 degrees. This is why AOB is again 150 degrees and ACB will be half that measurement.
1. notice that angle AOB and angle ACB subtend the same minor arc: AB. Since this is the case, then ACB's measurement is a piece of cake (provided you know the theorem, of course). ACB will be 2 times smaller than AOB, since ACB has its vertex on the circle and AOB has its vertex in the origin. This makes ACB 75 degrees.
2. Again, we use the property outlined above, except that in this case we need to find out the measurement of AOB.
AOB subtends minor arc AB of 10pi/3. The total length of the circle is 2Pi*radius = 2*4*Pi = 8Pi and corresponds to the whole circle of 360 degrees. You get:
8Pi...............360 degrees
10Pi/3...........x degrees
x will be [(10Pi/3)*360]/8Pi = 150 degrees. This is why AOB is again 150 degrees and ACB will be half that measurement.
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cubicle_bound_misfit
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