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# In triangle ABC, AB has a length of 10 and D is the midpoint

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Math Expert
Joined: 02 Aug 2009
Posts: 7212
In triangle ABC, AB has a length of 10 and D is the midpoint  [#permalink]

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21 Dec 2009, 12:11
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Difficulty:

75% (hard)

Question Stats:

46% (01:41) correct 54% (01:46) wrong based on 260 sessions

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In triangle ABC, AB has a length of 10 and D is the midpoint of AB. What is the length of line segment DC?

(1) Angle C= 90
(2) Angle B= 45

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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Math Expert
Joined: 02 Sep 2009
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21 Dec 2009, 12:44
8
chetan2u wrote:
can the pt mentioned abt property of right angle triangle be proven

Imagine the right triangle inscribed in circle. We know that if the right triangle is inscribed in circle, hypotenuse must be diameter, hence half of the hypotenuse is radius. The line segment from the third vertex to the center is on the on the one hand radius of the circle=half of the hypotenuse and on the other hand as it's connecting the vertex with the midpoint of the hypotenuse it's median too.

Attachment:

Math_Tri_inscribed.png [ 6.47 KiB | Viewed 7823 times ]

Hope it's clear.
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##### General Discussion
Math Expert
Joined: 02 Sep 2009
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21 Dec 2009, 12:26
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2
chetan2u wrote:
In triangle ABC, AB has a length of 10 and D is the midpoint of AB. What is the length of line segment DC?

(1) Angle C= 90
(2) Angle B= 45

(1) We have right triangle ABC, with right angle at C. Property of right triangle: median from right angle is half of the hypotenuse, hence CD=AB/2=10/2=5. Sufficient.

(2) Clearly insufficient.

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21 Dec 2009, 12:30
2
can the pt mentioned abt property of right angle triangle be proven
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Manager
Joined: 21 Jul 2003
Posts: 58

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21 Dec 2009, 12:36
2
Can you please explain "Property of right triangle: median from right angle is half of the hypotenuse, hence CD=AB/2=10/2=5" in more detail.
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Joined: 21 Jul 2003
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21 Dec 2009, 12:49
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Excellent, and thank you for explaining
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Joined: 24 Jul 2009
Posts: 171
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Schools: Mellon, USC, MIT, UCLA, NSCU

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09 Jan 2010, 20:59
1
Bunuel wrote:
chetan2u wrote:
can the pt mentioned abt property of right angle triangle be proven

Imagine the right triangle inscribed in circle. We know that if the right triangle is inscribed in circle, hypotenuse must be diameter, hence half of the hypotenuse is radius. The line segment from the third vertex to the center is on the on the one hand radius of the circle=half of the hypotenuse and on the other hand as it's connecting the vertex with the midpoint of the hypotenuse it's median too.

Attachment:
Math_Tri_inscribed.png

Hope it's clear.

Thank you for the explanation. The inscribed triangle example helped a lot. Regarding STMT 1, my thought process was that the triangle could be 45-45-90 or 30-60-90, which in my mind, could affect the length of CD. However, from your example or more so the visual, I see that the angles don't matter...that the median is determined by the hypotenuse. Thanks for the lesson learned; basic yet important.
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Joined: 30 May 2013
Posts: 3
Re: In triangle ABC, AB has a length of 10 and D is the midpoint  [#permalink]

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15 Sep 2013, 22:14
Brilliant question.
SVP
Joined: 06 Sep 2013
Posts: 1705
Concentration: Finance
Re: In triangle ABC, AB has a length of 10 and D is the midpoint  [#permalink]

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03 Apr 2014, 07:49
I think I got this wrong. Let's see after drawing the figure we have a triangle with D written on AB side where AD and CD both have a length of 5 so we actually have two right triangles BDC and ADC.

In the second statement if B is 45 then BCD must also be 45 and hence we can calculate CD

Where am I going wrong here?
Thanks
Cheers
J
Math Expert
Joined: 02 Sep 2009
Posts: 52390
Re: In triangle ABC, AB has a length of 10 and D is the midpoint  [#permalink]

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03 Apr 2014, 08:32
jlgdr wrote:
I think I got this wrong. Let's see after drawing the figure we have a triangle with D written on AB side where AD and BD both have a length of 5 so we actually have two right triangles BDC and ADC.

In the second statement if B is 45 then BCD must also be 45 and hence we can calculate CD

Where am I going wrong here?
Thanks
Cheers
J

Notice that CD is the median, not the altitude, so we don't know whether triangles BDC and ADC are right angled.

Does this make sense?
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Manager
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Posts: 111
Re: In triangle ABC, AB has a length of 10 and D is the midpoint  [#permalink]

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18 May 2017, 21:19
It doesn't make sense - could you please elaborate on why (2) is NS?

Bunuel wrote:
jlgdr wrote:
I think I got this wrong. Let's see after drawing the figure we have a triangle with D written on AB side where AD and BD both have a length of 5 so we actually have two right triangles BDC and ADC.

In the second statement if B is 45 then BCD must also be 45 and hence we can calculate CD

Where am I going wrong here?
Thanks
Cheers
J

Notice that CD is the median, not the altitude, so we don't know whether triangles BDC and ADC are right angled.

Does this make sense?
Math Expert
Joined: 02 Sep 2009
Posts: 52390
Re: In triangle ABC, AB has a length of 10 and D is the midpoint  [#permalink]

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18 May 2017, 21:36
1
mdacosta wrote:
It doesn't make sense - could you please elaborate on why (2) is NS?

Bunuel wrote:
jlgdr wrote:
I think I got this wrong. Let's see after drawing the figure we have a triangle with D written on AB side where AD and BD both have a length of 5 so we actually have two right triangles BDC and ADC.

In the second statement if B is 45 then BCD must also be 45 and hence we can calculate CD

Where am I going wrong here?
Thanks
Cheers
J

Notice that CD is the median, not the altitude, so we don't know whether triangles BDC and ADC are right angled.

Does this make sense?

To put it simply: we know the length of a base (10) and one angle at the base (45 degrees). There are infinitely many triangles with this properties, so there are indefinitely many lengths of the median to the base possible.
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Re: In triangle ABC, AB has a length of 10 and D is the midpoint &nbs [#permalink] 18 May 2017, 21:36
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