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

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Math Expert
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% (01:23) correct 17% (01:59) wrong based on 58 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 753 times ]

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Director
Joined: 20 Feb 2015
Posts: 793
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
Director
Status: Learning stage
Joined: 01 Oct 2017
Posts: 892
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
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

Rise above the storm, you will find the sunshine

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Joined: 27 Oct 2017
Posts: 4
Location: United States
GPA: 3.59
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
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
1
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.
_________________

Regards,

PKN

Rise above the storm, you will find the sunshine

Intern
Joined: 27 Oct 2017
Posts: 4
Location: United States
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. &nbs [#permalink] 11 Aug 2018, 16:36
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