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# Circle Inscribed in a triangle-radius ?

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Manager
Affiliations: IIBA
Joined: 04 Sep 2010
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Location: India
Schools: HBS, Stanford, Stern, Insead, ISB, Wharton, Columbia
WE 1: Information Technology (Banking and Financial Services)
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00:00

Difficulty:

45% (medium)

Question Stats:

67% (01:12) correct 33% (01:07) wrong based on 36 sessions
What is the measure of the radius of the circle inscribed in a triangle whose sides measure 8, 15 and 17 units?

A. 8.5 units

B. 6 units

C. 3 units

D. 5 units

E. 12 units

Note: From the options provided, its easy to pick the answer right aways but I would want to know the computation steps.
[Reveal] Spoiler: OA

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Manager
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Re: Circle Inscribed in a triangle-radius ? [#permalink]  15 Jun 2011, 21:12
soaringAlone wrote:
What is the measure of the radius of the circle inscribed in a triangle whose sides measure 8, 15 and 17 units?

A. 8.5 units

B. 6 units

C. 3 units

D. 5 units

E. 12 units

Note: From the options provided, its easy to pick the answer right aways but I would want to know the computation steps.

Sides are 8, 15 and 17...thus it is right angle triangle Since 17^2 = 8^2 + 15^2
therefore, area = 1/2 * 15 * 8 = 60

Therefore, area of triangle = S*r ....where S=semi-perimeter and r= in-radius
Now S=semi-perimeter = 17+15+8 /2 = 20
Thus , 60 =20*r

Option C
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Re: Circle Inscribed in a triangle-radius ? [#permalink]  18 Jun 2011, 18:40
vyassa,

dint get it below part .Is thia some standard formulas for semi perimeter .

Therefore, area of triangle = S*r ....where S=semi-perimeter and r= in-radius
Now S=semi-perimeter = 17+15+8 /2 = 20
Thus , 60 =20*r
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Manager
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Re: Circle Inscribed in a triangle-radius ? [#permalink]  18 Jun 2011, 20:50
2
KUDOS
well there is a formula for area of the triangle and that is S*r....
In the given formula S is the semiperimeter i.e. half of the perimeter of the triangle. e.g. if a,b, and c are the sides of the triangle then perimeter will be a+b+c and semiperimeter will be (a+b+c)/2

Now, inradius is the radius of the circle that is inscribed in a triangle. In the given figure billow OP is an inradius.

Now, what all we know is three sides of the triangle, thus perimeter and area of triangle i.e. 60
Thus the easiest and fastest way is to apply the formula S*r = area of triangle
therefore, 20*r = 60 ...hence r = 3

Since r is the inradius i.e. radius of the inscribed circle, we have found out the answer.
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Manager
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Re: Circle Inscribed in a triangle-radius ? [#permalink]  18 Jun 2011, 21:09
Splendid!!KUDOS...............Innovative approach dude.
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Manager
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Re: Circle Inscribed in a triangle-radius ? [#permalink]  16 Jul 2011, 13:22
AnkitK, refer to Bunnel's post on Circles and Triangles.

Area = (P*r)/2 is a formula
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Re: Circle Inscribed in a triangle-radius ? [#permalink]  17 Jul 2011, 12:36
Thanks, I was not aware of this formula!
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Re: Circle Inscribed in a triangle-radius ? [#permalink]  18 Jul 2011, 02:35
puneetj wrote:
AnkitK, refer to Bunnel's post on Circles and Triangles.

Area = (P*r)/2 is a formula

This is same as s*r since p/2 = s
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Re: Circle Inscribed in a triangle-radius ?   [#permalink] 18 Jul 2011, 02:35
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