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Circum Radius of a triangle

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Circum Radius of a triangle [#permalink]

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New post 08 Jul 2011, 22:35
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23. What is the measure of the circum radius of a triangle whose sides are 9, 40 and 41?
A. 6
B. 4
C. 24.5
D. 20.5
E. 12.5


OPEN DISCUSSION OF THIS QUESTION IS HERE: http://gmatclub.com/forum/what-is-the-m ... 89583.html
[Reveal] Spoiler: OA

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Re: Circum Radius of a triangle [#permalink]

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New post 09 Jul 2011, 00:44
akkifreaky wrote:
23. What is the measure of the circum radius of a triangle whose sides are 9, 40 and 41?
A. 6
B. 4
C. 24.5
D. 20.5
E. 12.5


Can someone help me solve this !


In a right angled triangle, the circum radius is half of the hypotenuse.

hence its 41/2 = 20.5= D

In radius = ares/semi perimetr

Area = 1/2*40*9 = 180
semiperimter = (a+b+c)/2= (41+9+40)/2 = 90/2 = 45

inradius = 180/45 = 4

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Re: Circum Radius of a triangle [#permalink]

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New post 09 Jul 2011, 20:33
The moment the three numbers appear, a pythagorean triplet flashes in the mind. A small calculation confirms the inkling.

So now, we are talking about an angle in a semicircle. Basic geometry tells us that the angle in a semicircle is always a right angled triangle. Now make both ends meet. Since the right angled triangle is circumscribed the next obvious point is that the hypotenuse (which is also the longest side = 41) of this triangle must be the diameter. Hence the 20.5 is the right answer without a second thought. Hope this helps.

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Rahul
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Re: Circum Radius of a triangle [#permalink]

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Re: Circum Radius of a triangle [#permalink]

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New post 05 Sep 2017, 04:08
What is the measure of the radius of the circle that circumscribes a triangle whose sides measure 9, 40 and 41?
(A) 6
(B) 4
(C) 24.5
(D) 20.5
(E) 12.5

First of all we can notice that a triangle whose sides measure 9, 40 and 41 is a right triangle because 9^2 + 40^2 = 41^2.

Next, a right triangle inscribed in a circle must have its hypotenuse as the diameter of the circle (the reverse is also true: if the diameter of a circle is also the triangle’s side, then that triangle is a right triangle).

Thus the diameter of the circle is the hypotenuse of the triangle --> diameter = hypotenuse = 41 --> radius = 41/2 = 20.5.

Answer: D.

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Re: Circum Radius of a triangle   [#permalink] 05 Sep 2017, 04:08
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