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# In the figure above, line segments AB and AC are tangent to circle O.

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Joined: 02 Sep 2009
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In the figure above, line segments AB and AC are tangent to circle O.  [#permalink]

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02 Aug 2018, 00:45
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Difficulty:

25% (medium)

Question Stats:

83% (01:58) correct 17% (02:38) wrong based on 72 sessions

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In the figure above, line segments AB and AC are tangent to circle O. If the length of OB = 1 and the length of OA = √10, what is the area of quadrilateral ABOC? (Figure not drawn to scale.)

A. 3/2

B. √3

C. 2√2

D. 3

E. 2√3

Attachment:

Untitled.png [ 5.42 KiB | Viewed 1283 times ]

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Concentration: Strategy, General Management
Re: In the figure above, line segments AB and AC are tangent to circle O.  [#permalink]

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02 Aug 2018, 00:51
Bunuel wrote:

In the figure above, line segments AB and AC are tangent to circle O. If the length of OB = 1 and the length of OA = √10, what is the area of quadrilateral ABOC? (Figure not drawn to scale.)

A. 3/2

B. √3

C. 2√2

D. 3

E. 2√3

Attachment:
Untitled.png

angle ABO=angle ACO=90* (Property )
AB^2=10-1
AB=3
VP
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WE: Supply Chain Management (Energy and Utilities)
Re: In the figure above, line segments AB and AC are tangent to circle O.  [#permalink]

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02 Aug 2018, 04:02
1
Bunuel wrote:

In the figure above, line segments AB and AC are tangent to circle O. If the length of OB = 1 and the length of OA = √10, what is the area of quadrilateral ABOC? (Figure not drawn to scale.)

A. 3/2

B. √3

C. 2√2

D. 3

E. 2√3

Attachment:
Untitled.png

1) AB=AC (tangent property)
2) Angle OBA=90=Angle OCA
Area of quadrilateral ABOC= Area of triangle OBA+ Area of triangle OCA
Area of triangle OBA=Area of triangle OCA (from (1) and (3), and OA being the common side)
In the right angled triangle OBA, we have AB=$$\sqrt{10-1}$$=3
Area of triangle OBA=$$\frac{1}{2}*AB*OB$$=$$\frac{3}{2}$$
Area of quadrilateral=2*Area of triangle OBA=$$2*\frac{3}{2}$$=3

Ans. (D)
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PKN

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Re: In the figure above, line segments AB and AC are tangent to circle O.  [#permalink]

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09 Aug 2018, 17:28
1
PKN

How do we know that "Angle OBA=90=Angle OCA"?
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Re: In the figure above, line segments AB and AC are tangent to circle O.  [#permalink]

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09 Aug 2018, 21:09
2
RichardSaunders wrote:
PKN

How do we know that "Angle OBA=90=Angle OCA"?

Hi RichardSaunders,
By definition of tangent to a circle:-
Tangent is a line passing a circle and touching it at just one point.
The tangent line is always at the 90 degree angle (perpendicular) to the radius of a circle.
.

Here, the lines AB and AC touch the given circle at 'B' and 'C' respectively. Hence, they are tangents. As per above definition, the radii OB and OC are perpendicular to the lines AB and AC respectively. So, $$\angle{OBA}=90=\angle{OCA}$$

Hope it helps.
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Regards,

PKN

Rise above the storm, you will find the sunshine
Intern
Joined: 27 Oct 2017
Posts: 6
Location: United States
GMAT 1: 710 Q45 V42
GPA: 3.59
Re: In the figure above, line segments AB and AC are tangent to circle O.  [#permalink]

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11 Aug 2018, 16:36
Re: In the figure above, line segments AB and AC are tangent to circle O.   [#permalink] 11 Aug 2018, 16:36
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