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655-705 (Hard)|   Geometry|      
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firas92
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In the given figure, BC is the diameter of the circle. AB is a tangent 18 Aug 2020, 12:20
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55% (hard)

Question Stats:

67% (02:35) correct 33% (02:42) wrong based on 117 sessions

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In the given figure, BC is the diameter of the circle. AB is a tangent to the circle at point B. If the radius of the circle is 4 cm, then find the value of AC*DC.

A. 192
B. 128
C. 120
D. 64
E. 48
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D

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In the given figure, BC is the diameter of the circle. AB is a tangent 18 Aug 2020, 12:44
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BDC~ABC

\(\frac{DC}{BC} = \frac{BC}{AC}\)

\(AC*DC = BC^2 = 64\)
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In the given figure, BC is the diameter of the circle. AB is a tangent 23 Aug 2020, 05:08
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why can we conclude that the triangles are similar?
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nick1816
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In the given figure, BC is the diameter of the circle. AB is a tangent 23 Aug 2020, 05:41
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angle BDC = angle ABC = 90*

angle C is common in both triangles

Using AA criterion, we can say that both triangles are similar.

chrtpmdr
why can we conclude that the triangles are similar?
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In the given figure, BC is the diameter of the circle. AB is a tangent 23 Aug 2020, 06:32
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If this weren't a GMAT question (so we had no answer choices, or needed to prove why the answer is what it is), I'd solve the way nick did above, but if it is a GMAT question, we can solve without doing much work:

If this question has just one answer, then the answer must be the same no matter where point D is. If the answer changed when we moved point D around, one of the answer choices would need to be "cannot be determined". So we can freely put point D anywhere we like. If we put point D so it is millimeters away from point B (so the length of line AB is almost zero), then AC and DC will both almost be identical to the diameter of the circle, and will both therefore be almost exactly 8 units long. So their product will be extremely close (or equal) to 64, and that's the only plausible answer choice.
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In the given figure, BC is the diameter of the circle. AB is a tangent 12 Aug 2022, 12:24
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Need to clarify how sides are in ratio….how it is been assumed that sides AB = BC

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In the given figure, BC is the diameter of the circle. AB is a tangent 23 Aug 2022, 09:04
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khedikarmohashin
Need to clarify how sides are in ratio….how it is been assumed that sides AB = BC

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WE CAN CONSIDER OTHER TRIANGLES AS SIMILAR TO GET THE SOLUTION. HAVE A LOOK AT THE PICTURE.
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