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

Question

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

Princ · Answer

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. main-qimg-1df9f479345f05bdedf2db171912a46a.png 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

GMATinsight · Answer

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

GMATinsight · Answer

For other readers (Who are already less confident in Quant):

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

bumpbot · Answer

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

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