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Re: IN TRIANGLE ABC [#permalink]
21 Dec 2010, 07:31

10

This post received KUDOS

Expert's post

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Attachment:

trig2uc8.png [ 9.64 KiB | Viewed 18398 times ]

In triangle ABC above, what is the length of side BC?

As <BDC=<BCD then the BD=BC. Also as <ADB=180-2x (exterior angle) and the sum of the angles of a triangle is 180 degrees then in triangle ADB we'll have: x+(180-2x)+<ABD=180 --> <ABD=x. Now, we have that <ABD=x=<DAB so AD=BD --> AD=BD=BC.

Question: BC=?

(1) Line segment AD has length 6 --> AD=BD=BC=6. Sufficient. (2) x = 36 --> we know only angles which is insufficient to get the length of any line segment.

Re: IN TRIANGLE ABC [#permalink]
26 Feb 2011, 23:52

1

This post received KUDOS

Expert's post

vibhav wrote:

the one point that puzzles me is how did you get /BAD = x ?

It's given that <BAD=x degrees (refer to the diagram in my first post on the page). Some OG books have a typo missing this info (as in vibhav post). _________________

The question asks the length of side BC. From the figure, you can see that triangle BDC is an isosceles triangle with BD = BC. Thus, to know the length of BC, it is okay if we know the length of BD.

Statement 1: To solve such problems, you have to know that in a triangle, the measure of the exterior angle is equal to the sum of the two non-adjacent angles of the triangle.

That is, in the given figure, for triangle ABD, angle BDC is the exterior angle. Thus, BDC = ABD + BAD That is, 2x = ABD + x. Thus ABD = x.

Now, you can see that triangle ABD is an isosceles triangle in which AD = BD = 6. Thus, BD = BC = 6. SUFFICIENT

Statement 2: x = 36 does not tell you anything about the length of any side. INSUFFICIENT

Re: Triangle Problem [#permalink]
20 Mar 2012, 18:09

Using Similar triangles we know that 1) BD = BC (angle BDC = angle BCD) 2) We know angle BDA = 180-2x which means angle ABD = x 3) So, from the second similar triangle we know that angle BAD = angle ABD = x 4) Using similar triangles again; AD = BD 5) Combing 1 and 4; AD = BD = BC.

Re: In triangle ABC above, what is the length of side BC? [#permalink]
23 Apr 2014, 21:48

Expert's post

jlgdr wrote:

Why is AD=BD=BC? If AD is opposite to X, BD opposite to X as well and BC opposite to 2x? Shouldn't BC be larger than both or equal to both TOGETHER?

Thanks for clarifying

Cheers! J

Yes but they are sides of different triangles. Note that by the same logic, BD is opposite to 2x as well. The point is that it is opposite to x in one triangle (ABD) and opposite to 2x in another triangle (BDC).

BC will be equal to BD because they are both opposite 2x in triangle BDC.

AD will be equal to BD because they are both opposite angle x in triangle ABD.

Re: In triangle ABC above, what is the length of side BC? [#permalink]
20 Jun 2014, 02:35

Bunuel wrote:

Attachment:

trig2uc8.png

In triangle ABC above, what is the length of side BC?

As <BDC=<BCD then the BD=BC. Also as <ADB=180-2x (exterior angle) and the sum of the angles of a triangle is 180 degrees then in triangle ADB we'll have: x+(180-2x)+<ABD=180 --> <ABD=x. Now, we have that <ABD=x=<DAB so AD=BD --> AD=BD=BC.

Question: BC=?

(1) Line segment AD has length 6 --> AD=BD=BC=6. Sufficient. (2) x = 36 --> we know only angles which is insufficient to get the length of any line segment.

Answer: A.

Thanks for the answer... I guess I need to expand my thought process... _________________

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