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# If angle BAD is a right angle, what is the length of side

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If angle BAD is a right angle, what is the length of side [#permalink]

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23 Jan 2010, 16:43
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If angle BAD is a right angle, what is the length of side BD?

(1) AC is perpendicular to BD
(2) BC = CD

[Reveal] Spoiler:

Source MGMAT Geometry Question Bank

From (2), can I automatically infer that AC is a bisector?

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-angle-bad-is-a-right-angle-what-is-the-length-of-side-105559.html
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Re: What is the hypotenuse? [#permalink]

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23 Jan 2010, 16:50
How is BAD an isoceles triangle? I do not understand MGMAT's explanation.
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Re: What is the hypotenuse? [#permalink]

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23 Jan 2010, 17:13
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gottabwise wrote:
If angle BAD is a right angle, what is the length of side BD?

(1) AC is perpendicular to BD
(2) BC = CD

[Reveal] Spoiler:

Source MGMAT Geometry Question Bank

From (2), can I automatically infer that AC is a bisector?

From the given figure,

when AC is perpendicular to BD, we won't be able to figure out anything about the triangles or the associated angles and we can't calculate what could possibly be the length of BD.

When BC = CD, C is mid-point of BD and AC is the median, still we can't comment on the length of BD in any possible way.

When both the given statements are considered together, we immediately realize that AC is both the angular bisector of A and altitude of the given triangle BAD. So we split BAD into two equally sized triangles BAC and ACD, such that AD = AB = 5. So, BD is obviously the full-hypotenuse of BAD and length is thus sqrt(2)*5.
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Re: What is the hypotenuse? [#permalink]

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23 Jan 2010, 20:18
BarneyStinson wrote:
gottabwise wrote:
If angle BAD is a right angle, what is the length of side BD?

(1) AC is perpendicular to BD
(2) BC = CD

[Reveal] Spoiler:

Source MGMAT Geometry Question Bank

From (2), can I automatically infer that AC is a bisector?

From the given figure,

when AC is perpendicular to BD, we won't be able to figure out anything about the triangles or the associated angles and we can't calculate what could possibly be the length of BD.

When BC = CD, C is mid-point of BD and AC is the median, still we can't comment on the length of BD in any possible way.

When both the given statements are considered together, we immediately realize that AC is both the angular bisector of A and altitude of the given triangle BAD. So we split BAD into two equally sized triangles BAC and ACD, such that AD = AB = 5. So, BD is obviously the full-hypotenuse of BAD and length is thus sqrt(2)*5.

Thank you for the clear explanation. It helped a great deal.
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Re: If angle BAD is a right angle, what is the length of side [#permalink]

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24 Jan 2013, 07:21
Hi Bunuel/Karishma

I still don't understand how BAD is an isoceles triangle?

Kindly help..
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Re: If angle BAD is a right angle, what is the length of side [#permalink]

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24 Jan 2013, 07:24
Sachin9 wrote:
Hi Bunuel/Karishma

I still don't understand how BAD is an isoceles triangle?

Kindly help..

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-angle-bad-is-a-right-angle-what-is-the-length-of-side-105559.html

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Re: If angle BAD is a right angle, what is the length of side   [#permalink] 24 Jan 2013, 07:24
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