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If AC=12, does ACB=90?

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If AC=12, does ACB=90? [#permalink]

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New post Updated on: 15 Mar 2018, 23:07
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  55% (hard)

Question Stats:

55% (00:34) correct 45% (00:53) wrong based on 38 sessions

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If AC = 12, does ACB = 90?


(1) BC = 5
(2) AC=CD

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Originally posted by itisSheldon on 15 Mar 2018, 08:39.
Last edited by Bunuel on 15 Mar 2018, 23:07, edited 1 time in total.
Edited the question.
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Re: If AC=12, does ACB=90? [#permalink]

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New post 15 Mar 2018, 23:04
itisSheldon wrote:
If AC=12, does ACB=90?
Attachment:
Capture1.JPG


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
Re: If AC=12, does ACB=90?   [#permalink] 15 Mar 2018, 23:04
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