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15 Apr 2018, 00:11
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
67% (01:41) correct
33%
(01:29)
wrong
based on 9
sessions
History
Date
Time
Result
Not Attempted Yet
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
(A) 2 units
(B) 12 units
(C) 6.5 units
(D) 6 units
(E) 7.5 units
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itisSheldon
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 54801 times ]
Moderator Note: 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
Updated on: 15 Apr 2018, 04:59
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.
Last edited by GMATinsight on 15 Apr 2018, 04:59, edited 2 times in total.
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itisSheldon
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
Answer: option A
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File comment: www.GMATinsight.com
circle_within_right_tri_sol.gif [ 2.19 KiB | Viewed 7083 times ]
