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
Inscribed circle in triangle - To find angle ABC
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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
Your logic would be 100% perfect IF it were the case that DE is the diameter. However, we can't conclude this.
Cheers,
Brent
GMAT/MBA Expert
- Brent@GMATPrepNow
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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
Last edited by Brent@GMATPrepNow on Mon Apr 16, 2018 1:15 pm, edited 1 time in total.
- Paras_0111
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Hi Brent - Can you please help me understand how in Case A, ABC becomes a right angle?
Regards,
Paras
Regards,
Paras