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# M70-24

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Math Expert
Joined: 02 Sep 2009
Posts: 56269

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03 Sep 2018, 05:51
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Difficulty:

45% (medium)

Question Stats:

50% (01:37) correct 50% (00:34) wrong based on 8 sessions

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If AB is a tangent to the circle above, what is ∠ACD?

(1) DE is a diameter

(2) ∠CDE = ∠CED

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Joined: 02 Sep 2009
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03 Sep 2018, 05:52
Official Solution:

We’ll go for ALTERNATIVE since we can play with the figure to eliminate the wrong answers.

(1) ∠ECD is an inscribed angle facing a diameter, meaning that it equals 90°, but moving point D closer to or farther from point C shows us that the size of ∠ACD can change – not enough! (A) and (D) are eliminated.

(2) The two equal angles mean that the triangle is an isosceles. This means that, due to symmetry, ∠ACD = ∠BCE − but that’s not enough in order to determine their size. (B) is eliminated.

If we combine the two statements, ∠ACD + ∠BCE = 90˚, and since they are both equal, each of them is 45˚ − that’s enough! (E) is eliminated.

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13 Sep 2018, 18:20
Bunuel wrote:
Official Solution:

(1) ∠ECD is an inscribed angle facing a diameter, meaning that it equals 90°, but moving point D closer to or farther from point C shows us that the size of ∠ACD can change – not enough! (A) and (D) are eliminated.

Hi Bunuel,

What do you mean by moving point D closer to or farther from point C? if DE is the diameter and C is in the tangent shoulnd't both angles be the same? I mean, doesn't statement 1 give enough evidence to conclude what statement 2 says?

thanks!
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Joined: 07 Oct 2017
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13 Sep 2018, 22:43
tsuxinhah wrote:
Bunuel wrote:
Official Solution:

(1) ∠ECD is an inscribed angle facing a diameter, meaning that it equals 90°, but moving point D closer to or farther from point C shows us that the size of ∠ACD can change – not enough! (A) and (D) are eliminated.

Hi Bunuel,

What do you mean by moving point D closer to or farther from point C? if DE is the diameter and C is in the tangent shoulnd't both angles be the same? I mean, doesn't statement 1 give enough evidence to conclude what statement 2 says?

thanks!
Hi tsuxinhah

For Geometry DS, always try to imagine if we can restrict the figure in one orientation. For statement 1, diameter is restricted but point C can lie on any point in the circumference as it is not restricted by the given condition.

This will in turn keep changing the desired angle and hence statement is not sufficient.

Thank you = Kudos
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Joined: 16 Sep 2018
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30 Sep 2018, 23:03
Answer C is only correct if we know that AB is parallel to DE. But we dont know that for sure so answer E.
Or can someone pls tell me if a made a mistake?

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01 Oct 2018, 01:31
Phibo wrote:
Answer C is only correct if we know that AB is parallel to DE. But we dont know that for sure so answer E.
Or can someone pls tell me if a made a mistake?

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St : 1 DE is diameter

St 2 : Angle CDE and CED are equal.

Now Point C is on circle.

So angle C is 90 degrees.

Angle CDE and Angle CED = 45 degrees.

So DE parallel to line ACB.

Does this help?
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Joined: 16 Sep 2018
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01 Oct 2018, 01:51
Thanks for your quick reply. Sry I totally missed the fact that C has to be the tanget point of AB. Otherwise the test cant ask for the ACD-angle.
thx again

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Re: M70-24   [#permalink] 01 Oct 2018, 01:51
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# M70-24

Moderators: chetan2u, Bunuel