itisSheldon wrote:

If AC=12, does ACB=90?

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1) BC = 5

2) AC=CD

Statement 1:

With AC=12 and BC=5, but without knowing the length of AB, we cannot conclude whether angle ACB is 90 or not. IF AB=13, then the triangle will have the sides as (5,12,13) which is a pythagorean triplet, and it will become a right angled triangle. But without that this statement is

not sufficient.

Statement 2:

IF AC=CD, this means BC is a median. But that doesn't help us in figuring out angle ACB.

Not sufficient.

Combining the statements:

AC=CD=12 and BC which is median is 5. But without knowing anything about sides AB/BD we cannot conclude what angle ACB will be. Eg, if it was given that triangle is isosceles with AB=BD then we would have concluded that angle ACB=90 (because in that case median would be perpendicular to the opposite side). But since that also is not given, even after combining the statements the data is

not sufficient.

Hence

E answer