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If in the figure above, AB is tangent to the circle centered at C, wha

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Bunuel
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If in the figure above, AB is tangent to the circle centered at C, wha [#permalink] New post   06 May 2021, 01:30
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If in the figure above, AB is tangent to the circle centered at C, what is the area of triangle ABC?

(1) AB=10
(2) The circumference of the circle is 15.


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Re: If in the figure above, AB is tangent to the circle centered at C, wha [#permalink] New post   07 May 2021, 01:15
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Bunuel wrote:

If in the figure above, AB is tangent to the circle centered at C, what is the area of triangle ABC?

(1) AB=10
(2) The circumference of the circle is 15.


Project DS Butler Data Sufficiency (DS3)


For DS butler Questions Click Here


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Attachment:
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Since AB is tangent to the circle, then radius from C to the tangent point is perpendicular to AB, therefore the area is 1/2*height*AB = 1/2*radius*AB.

First statement gives AB and second statement gives the radius, so together the statements are sufficient to get the area.

Answer: C.

Hope it helps.
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If in the figure above, AB is tangent to the circle centered at C, wha [#permalink] New post   06 May 2021, 02:39
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If in the figure above, AB is tangent to the circle centered at C, what is the area of triangle ABC?

Stat1: AB=10
Not sufficient, as we don't have value of radius.

Stat2: The circumference of the circle is 15.
Not sufficient, we need side value of triangle ABC also.

Combining both, area triangle ABC= 1/2 * Base * height; we have base = AB and radius is known from stat2. Sufficient.

Note- Here, height = Radius of circle.

So, I think C. :)
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Re: If in the figure above, AB is tangent to the circle centered at C, wha [#permalink] New post   06 May 2021, 03:06
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Bunuel wrote:

If in the figure above, AB is tangent to the circle centered at C, what is the area of triangle ABC?

(1) AB=10
(2) The circumference of the circle is 15.


Project DS Butler Data Sufficiency (DS3)


For DS butler Questions Click Here


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Attachment:
1.png



Statement :1 AB=10
Base is known, but height is not known
Not sufficient

Statement : 2 The circumference of the circle is 15.
Radius can be calculated i.e height of the triangle is known as Radius wil be perpendicular to the tangent and will be equal to height of the triangle but base is not known
Not sufficient

Combined
Height and base of the triangle are known hence, sufficient
C is the answer
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Re: If in the figure above, AB is tangent to the circle centered at C, wha [#permalink] New post   06 May 2021, 04:45
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If in the figure above, AB is tangent to the circle centered at C, what is the area of triangle ABC?

(1) AB=10
Since the radius of the circle i.e. height of the triangle is not fixed, the area is not fixed.
Not sufficient

(2) The circumference of the circle is 15.
Now, the height of the triangle is fixed, but not its base.
Not sufficient

(1) + (2)
Height and base of the triangle are known. We, have a unique triangle.
Sufficient

Option C

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Re: If in the figure above, AB is tangent to the circle centered at C, wha [#permalink]
06 May 2021, 04:45
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