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
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  • Lap #[LAPCOUNT] ([LAPTIME])
    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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    Post 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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    Post Sat Feb 15, 2014 9:25 am
    gmattesttaker2 wrote:


    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:

    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:

    Here, DE is parallel to BC, and AB = BC. In this case, angle ABC is a right angle.

    Case b:

    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

    _________________
    Brent Hanneson – Founder of GMATPrepNow.com
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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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