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Inscribed circle in triangle - To find angle ABC

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Inscribed circle in triangle - To find angle ABC

by gmattesttaker2 » Sat Feb 15, 2014 1:16 am
Hello,

Can you please assist with this:

A circle is inscribed in triangle ABC. If point D lies on side AB, is angle ABC a
right angle?

(1) DE is parallel to BC
(2) AB = BC

OA: E

I thought that the answer should be A since DE is the diameter hence angle BDE = 90 degrees. If DE is parallel to BC then angle ABC is 90 degrees as well.

Can you please help?

Thanks,
Sri
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Source: — Data Sufficiency |

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by Brent@GMATPrepNow » Sat Feb 15, 2014 1:23 am
Hey Sri,

Your logic would be 100% perfect IF it were the case that DE is the diameter. However, we can't conclude this.

Cheers,
Brent
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Inscribed circle in triangle - To find angle ABC

by Brent@GMATPrepNow » Sat Feb 15, 2014 9:25 am
gmattesttaker2 wrote: Image

A circle is inscribed in triangle ABC. If point D lies on side AB, is angle ABC a right angle?

(1) DE is parallel to BC
(2) AB = BC
Target question: Is angle ABC a right angle?

IMPORTANT: The primary purpose of the circle is to make the test-taker draw unfounded conclusions about the line DE. In actuality, the circle does not add any useful information to this question, so let's see what happens if we ignore it:
Image
Once we ignore the circle and scan the two statements, we might start to get the feeling that neither statement helps us determine whether or not angle ABC is a right angle.
So, we might start looking for some counter-examples that meet the conditions in both statements yet yield conflicting answers to the target question.

Statements 1 and 2 combined
There are several triangles that satisfy the conditions in BOTH statements. Here are two:
Case a:
Image
Here, DE is parallel to BC, and AB = BC. In this case, angle ABC is a right angle.

Case b:
Image
Here, DE is parallel to BC, and AB = BC. In this case, angle ABC is not a right angle.

Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer = E

Cheers,
Brent
Last edited by Brent@GMATPrepNow on Mon Apr 16, 2018 1:15 pm, edited 1 time in total.
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by Paras_0111 » Wed Mar 08, 2017 11:43 am
Hi Brent - Can you please help me understand how in Case A, ABC becomes a right angle?

Regards,
Paras
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