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Circle Inscribed in a triangle-radius ?

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Circle Inscribed in a triangle-radius ? [#permalink] New post 15 Jun 2011, 20:43
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A
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E

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Question Stats:

68% (01:13) correct 32% (01:06) wrong based on 31 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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Re: Circle Inscribed in a triangle-radius ? [#permalink] New post 18 Jun 2011, 20:50
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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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Re: Circle Inscribed in a triangle-radius ? [#permalink] New post 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

We have to find in-radius
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
and hence r=in-radius= 3

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

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

We have to find in-radius
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
and hence r=in-radius= 3
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Re: Circle Inscribed in a triangle-radius ? [#permalink] New post 18 Jun 2011, 21:09
Splendid!!KUDOS...............Innovative approach dude.
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Re: Circle Inscribed in a triangle-radius ? [#permalink] New post 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] New post 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] New post 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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