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Triangle ABC is a right triangle. D is the midpoint of hypotenuse AC

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Intern
Joined: 24 Sep 2015
Posts: 4
Triangle ABC is a right triangle. D is the midpoint of hypotenuse AC  [#permalink]

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Updated on: 25 Sep 2015, 20:34
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Difficulty:

95% (hard)

Question Stats:

52% (02:15) correct 48% (01:35) wrong based on 46 sessions

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Triangle ABC is a right triangle. D is the midpoint of hypotenuse AC. BE is tangent to DC. What is DE?

1) AB=12
2) BE=9

Thank you!!

Originally posted by cjcj on 25 Sep 2015, 20:09.
Last edited by ENGRTOMBA2018 on 25 Sep 2015, 20:34, edited 1 time in total.
Renamed the topic and added the OA.
Math Expert
Joined: 02 Aug 2009
Posts: 7755
Re: Triangle ABC is a right triangle. D is the midpoint of hypotenuse AC  [#permalink]

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25 Sep 2015, 20:31
cjcj wrote:
Triangle ABC is a right triangle. D is the midpoint of hypotenuse AC. BE is tangent to DC. What is DE?

1) AB=12
2) BE=9

Thank you!!

Hi,
i believe the answer should be C....
the answer cannot be A,B or D as a single value cannot deduce any other value here..
in any right triangle with two sides given, where two sides could be any altitude or one side, two sides etc... most of the values can be deduced..
here too, all three sides can be found with given two values.. hypotenuse comes out as a negative value or 36..
so it is 36, lly other values can be deuced...
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Re: Triangle ABC is a right triangle. D is the midpoint of hypotenuse AC  [#permalink]

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25 Sep 2015, 21:18
How do you get the 36 number? Sorry...
Math Expert
Joined: 02 Aug 2009
Posts: 7755
Re: Triangle ABC is a right triangle. D is the midpoint of hypotenuse AC  [#permalink]

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26 Sep 2015, 03:09
cjcj wrote:
How do you get the 36 number? Sorry...

1)let hyp AC=x, so BC=x^2-12^2, AB is given as 12...
so $$area = 12*\sqrt{x^2-12^2}/2$$

2) now if hyp is taken as base the alt BE is given as 9..
so area will be 9*x/2..

the areas have to be same..
$$9*\frac{x}{2}=12*\sqrt{x^2-12^2}/2$$
you will get x as$$\frac{48}{\sqrt{7}}$$
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Re: Triangle ABC is a right triangle. D is the midpoint of hypotenuse AC  [#permalink]

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10 Oct 2015, 03:15
Can anyone please draw a figure for this question?
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Re: Triangle ABC is a right triangle. D is the midpoint of hypotenuse AC  [#permalink]

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30 Mar 2018, 10:29
What is meant by "BE is tangent to DC"?

chetan2u wrote:
cjcj wrote:
Triangle ABC is a right triangle. D is the midpoint of hypotenuse AC. BE is tangent to DC. What is DE?

1) AB=12
2) BE=9

Thank you!!

Hi,
i believe the answer should be C....
the answer cannot be A,B or D as a single value cannot deduce any other value here..
in any right triangle with two sides given, where two sides could be any altitude or one side, two sides etc... most of the values can be deduced..
here too, all three sides can be found with given two values.. hypotenuse comes out as a negative value or 36..
so it is 36, lly other values can be deuced...

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Joined: 09 Aug 2017
Posts: 341
Re: Triangle ABC is a right triangle. D is the midpoint of hypotenuse AC  [#permalink]

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30 Mar 2018, 17:18
BE is tangent to DC...what does this mean?
Is BE is arc and where does E lie?
Re: Triangle ABC is a right triangle. D is the midpoint of hypotenuse AC   [#permalink] 30 Mar 2018, 17:18
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