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Inscribed circle in triangle - To find angle ABC

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gmattesttaker2 Legendary Member Default Avatar
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Inscribed circle in triangle - To find angle ABC

Post 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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Paras_0111 Junior | Next Rank: 30 Posts
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Post 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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Post Sat Feb 15, 2014 9:25 am
gmattesttaker2 wrote:
ttp://postimg.org/image/r3kh3ymwd/" target="_blank">

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:
ttp://postimg.org/image/ygzv2x6y5/" target="_blank">
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:
ttp://postimg.org/image/bw4hjlv1p/" target="_blank">
Here, DE is parallel to BC, and AB = BC. In this case, angle ABC is a right angle.

Case b:
ttp://postimg.org/image/4dlcaz3ot/" target="_blank">
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

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Paras_0111 Junior | Next Rank: 30 Posts
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Post 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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