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Intern  Affiliations: IIBA
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What is the measure of the radius of the circle inscribed in a triangl  [#permalink]

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Difficulty:   55% (hard)

Question Stats: 65% (01:53) correct 35% (01:42) wrong based on 130 sessions

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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.
Manager  Joined: 07 Oct 2010
Posts: 125
Re: What is the measure of the radius of the circle inscribed in a triangl  [#permalink]

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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
##### General Discussion
Manager  Joined: 11 Feb 2011
Posts: 104
Re: What is the measure of the radius of the circle inscribed in a triangl  [#permalink]

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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
Manager  Joined: 07 Oct 2010
Posts: 125
Re: What is the measure of the radius of the circle inscribed in a triangl  [#permalink]

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2
2
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  Joined: 11 Feb 2011
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Re: What is the measure of the radius of the circle inscribed in a triangl  [#permalink]

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Splendid!!KUDOS...............Innovative approach dude.
Manager  Joined: 08 Sep 2010
Posts: 89
Re: What is the measure of the radius of the circle inscribed in a triangl  [#permalink]

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AnkitK, refer to Bunnel's post on Circles and Triangles.

Area = (P*r)/2 is a formula
Manager  Joined: 14 Apr 2011
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Re: What is the measure of the radius of the circle inscribed in a triangl  [#permalink]

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Thanks, I was not aware of this formula!
Manager  Joined: 07 Oct 2010
Posts: 125
Re: What is the measure of the radius of the circle inscribed in a triangl  [#permalink]

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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: What is the measure of the radius of the circle inscribed in a triangl  [#permalink]

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3
1
This can be solved with linear equations (with 3 variables).

Lets assume AB=8, BC=15 and AC=17.

Here we can have a+b=8, b+c=15 and a+c=17 (as per tangents intersection)
b+c=15
-a+b=8
---------
c-a=7

c-a=7
c+a=17
---------
2c=24 or c=12 hence b=3
Attachments P2 20151219.png [ 7.11 KiB | Viewed 20872 times ]

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Re: What is the measure of the radius of the circle inscribed in a triangl  [#permalink]

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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.

Area of △ is $$\sqrt{s ( s - a )( s - b )( s - c )}$$ ; $$s = a+b+c/2$$

$$s = 8+15+17/2$$

Or, $$s = 20$$

So, Area = $$\sqrt{20( 20 - 8 )( 20 - 15 )( 20 - 17 )}$$

Or, Area = $$\sqrt{20*12*5*3}$$

Or, Area = $$\sqrt{20*12*5*3}$$

Or, Area = $$60$$

Radius of Incentre = $$\frac{Area}{s}$$

Radius of Incentre = $$\frac{60}{20}$$

Radius of Incentre = $$3$$

Hence, answer will be (C) 3

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Abhishek....

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GMAT 1: 620 Q46 V29 Re: What is the measure of the radius of the circle inscribed in a triangl  [#permalink]

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I believe subject problem can be solved in easier way.
IAW properties of right triangles, radius of inscribed circle equals to sum of minor sides plus hypotenuse and the result devided by 2, so in this case it would be as follows:
(8+15-17)/2 = 3
Ans C
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Re: What is the measure of the radius of the circle inscribed in a triangl  [#permalink]

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I don't know whether it's necessary to know the relationship between an inscribed circle's radius and the right triangle it is inscribed in - however, i just wanted to mention that this particular problem could be solved thorough reasoning alone.

Just make your simplest possible possible 8-15-17 right triangle, let the short leg be the altitude. From here, the inscribed circle can't possibly have a diameter larger or equal to eight, as it wouldn't fit inside the triangle in that case. Thus the radius must be smaller than 4. We can conclude that 3 is the right answer.
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Re: What is the measure of the radius of the circle inscribed in a triangl  [#permalink]

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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

circle inscribed in a right triangle (8:15:17) has radius:
r=(a+b-hyp)/2=(8+15-17)/2=3
r=area/semiperimeter=(ab/2)/[(a+b+c)/2]=8*15/40=3

Ans (C) Re: What is the measure of the radius of the circle inscribed in a triangl   [#permalink] 24 Jan 2020, 06:20
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