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# What is the radius of the incircle of the triangle whose sides measure

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Joined: 03 Mar 2018
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What is the radius of the incircle of the triangle whose sides measure  [#permalink]

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15 Apr 2018, 00:11
1
00:00

Difficulty:

35% (medium)

Question Stats:

92% (00:51) correct 8% (02:10) wrong based on 13 sessions

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What is the radius of the incircle of the triangle whose sides measure 5, 12 and 13 units?

(A) 2 units
(B) 12 units
(C) 6.5 units
(D) 6 units
(E) 7.5 units

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Joined: 22 Feb 2018
Posts: 325
What is the radius of the incircle of the triangle whose sides measure  [#permalink]

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Updated on: 15 Apr 2018, 05:21
1
1
itisSheldon wrote:
What is the radius of the incircle of the triangle whose sides measure 5, 12 and 13 units?

(A) 2 units
(B) 12 units
(C) 6.5 units
(D) 6 units
(E) 7.5 units

itisSheldon
As 5,12 and 13 are pythagorean triplet ,so It is a right angled triangle.
Radius of Incircle of Right angled triangle is given r =$$\frac{(a+b-c)}{2}$$
Where c is hypotenuse, a and b are other two sides.
Attachment:

main-qimg-1df9f479345f05bdedf2db171912a46a.png [ 19.14 KiB | Viewed 8434 times ]

Edit: Reason for AE=AD and EC=CF: length of tangents drawn from an external point to a circle are equal

here putting c = 13, a=5 , b= 12, we get r =$$\frac{(5+12-13)}{2}$$$$=2$$
OA=A
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Originally posted by Princ on 15 Apr 2018, 03:17.
Last edited by Princ on 15 Apr 2018, 05:21, edited 1 time in total.
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Joined: 08 Jul 2010
Posts: 2334
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What is the radius of the incircle of the triangle whose sides measure  [#permalink]

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Updated on: 15 Apr 2018, 04:59
itisSheldon wrote:
What is the radius of the incircle of the triangle whose sides measure 5, 12 and 13 units?

(A) 2 units
(B) 12 units
(C) 6.5 units
(D) 6 units
(E) 7.5 units

Incircle, CircumCircle are not the terms that GMA Uses

As represented in figure, AB = 5, BC = 12, AC = 13

First we need to notice that the triangle is a right triangle

Now since the two tangents drawn from the same point on any circle are equal therefore
BP = BN = Radius r
CN = CM = 12-r
AP = AM = 5-r

Also, AM + CM = 13
i.e. (5-r) + (12-r) = 13

i.e. r = 2

Attachments

File comment: www.GMATinsight.com

circle_within_right_tri_sol.gif [ 2.19 KiB | Viewed 281 times ]

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Originally posted by GMATinsight on 15 Apr 2018, 04:55.
Last edited by GMATinsight on 15 Apr 2018, 04:59, edited 2 times in total.
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Joined: 08 Jul 2010
Posts: 2334
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Re: What is the radius of the incircle of the triangle whose sides measure  [#permalink]

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15 Apr 2018, 04:58
itisSheldon wrote:
What is the radius of the incircle of the triangle whose sides measure 5, 12 and 13 units?

(A) 2 units
(B) 12 units
(C) 6.5 units
(D) 6 units
(E) 7.5 units

Please do NOT bother yourself with learning the formula for Inradius and Circumradius. They are beyond GMAT Scope...

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e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

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Re: What is the radius of the incircle of the triangle whose sides measure &nbs [#permalink] 15 Apr 2018, 04:58
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# What is the radius of the incircle of the triangle whose sides measure

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