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M24 Q22

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Intern
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Joined: 18 Jan 2010
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M24 Q22 [#permalink]

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New post 04 May 2010, 08:38
In triangle ABC, point O lies on side AC and segment BO is perpendicular to AC. If angle BAO = angle BCA = 45 degrees and BC=1, what is the area of triangle ABO?

1/4
1/2
1
radical2
2

Please explain in details.
Thanks in advance

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Senior Manager
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Joined: 25 Jun 2009
Posts: 298

Kudos [?]: 151 [0], given: 6

Re: M24 Q22 [#permalink]

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New post 05 May 2010, 11:08
gmat00 wrote:
In triangle ABC, point O lies on side AC and segment BO is perpendicular to AC. If angle BAO = angle BCA = 45 degrees and BC=1, what is the area of triangle ABO?

1/4
1/2
1
radical2
2

Please explain in details.
Thanks in advance


Refer the attached figure.,

Angle ABC = 90, BO is the prependicular to side AC and hence it will also be the prependicular bisector for the side AC ( as angles BAO = BCA = 45)

this also implies that angle ABO =CBO = 45 hence CO=BO=AO = X

hyp theorm \(x^2 + x^2 = 1\)
\(x^2= \frac{1}{2}\)

\(x= \frac{1}{\sqrt{2}}\)

Area of trianle ABO =\(\frac{1}{2} * AO* BO\)

Area = \(\frac{1}{2} * x^2\)= \(\frac{1}{2} *\frac{1}{2} = \frac{1}{4\)}
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Director
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Joined: 25 Aug 2007
Posts: 925

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WE 1: 3.5 yrs IT
WE 2: 2.5 yrs Retail chain
Re: M24 Q22 [#permalink]

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New post 05 May 2010, 11:18
1/4.

Since both the angles are 45 degrees, triangle ABC has to be a right angled triangled at B. So, AB = BC =1
Ar(ABC)=1/2x1x1 = 1/2

Therefore, Ar(ABO) = 1/2xAr(ABC) = 1/4.

gmat00 wrote:
In triangle ABC, point O lies on side AC and segment BO is perpendicular to AC. If angle BAO = angle BCA = 45 degrees and BC=1, what is the area of triangle ABO?

1/4
1/2
1
radical2
2

Please explain in details.
Thanks in advance

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Re: M24 Q22 [#permalink]

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New post 06 May 2010, 13:29
Thanks guys :-D

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Re: M24 Q22   [#permalink] 06 May 2010, 13:29
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