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# What is the measure of the radius of the circle inscribed in a triangl

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

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15 Jun 2011, 20:43
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55% (hard)

Question Stats:

66% (01:56) correct 34% (01:42) wrong based on 132 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.
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Re: What is the measure of the radius of the circle inscribed in a triangl  [#permalink]

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15 Jun 2011, 21:12
1
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: What is the measure of the radius of the circle inscribed in a triangl  [#permalink]

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19 Dec 2015, 01:46
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
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Re: What is the measure of the radius of the circle inscribed in a triangl  [#permalink]

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18 Jun 2011, 20:50
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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Re: What is the measure of the radius of the circle inscribed in a triangl  [#permalink]

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

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18 Jun 2011, 21:09
Splendid!!KUDOS...............Innovative approach dude.
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Re: What is the measure of the radius of the circle inscribed in a triangl  [#permalink]

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

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17 Jul 2011, 12:36
Thanks, I was not aware of this formula!
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Re: What is the measure of the radius of the circle inscribed in a triangl  [#permalink]

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

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31 Dec 2016, 08:51
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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Re: What is the measure of the radius of the circle inscribed in a triangl  [#permalink]

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19 Feb 2017, 23:13
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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22 Jul 2019, 01:35
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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24 Jan 2020, 06:20
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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# What is the measure of the radius of the circle inscribed in a triangl

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