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

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