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A circle circumscribes the triangle ABC

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A circle circumscribes the triangle ABC  [#permalink]

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New post Updated on: 08 Oct 2018, 07:48
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A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

64% (00:40) correct 36% (01:21) wrong based on 21 sessions

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A circle circumscribes the triangle ABC and length of the three sides of the triangle are 8 cm, 15 cm and 17 cm respectively.

Find out the radius of the circle.



A.4.5
B.7.5
C.8.5
D.10.5
E.Cannot be determined

Originally posted by nitesh50 on 08 Oct 2018, 06:17.
Last edited by nitesh50 on 08 Oct 2018, 07:48, edited 1 time in total.
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Re: A circle circumscribes the triangle ABC  [#permalink]

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New post Updated on: 08 Oct 2018, 07:25
nitesh50 wrote:
A circle circumscribes the triangle ABC and length of the three sides of the triangle are 8 cm, 15 cm and 17 cm respectively.

Find out the radius of the circle.



A.4.5
B.7.5
C.8.5
D.10.5
E.Cannot be determined



8, 15, 17 is a Pythagorean triplet. Hence, the triangle in question is a right triangle with 17 as hypotenuse, which in this case is the diameter of the circle. Thus, the radius of the circle will be 17/2 = 8.5.

C should be the correct option.

Originally posted by Ankit75 on 08 Oct 2018, 06:51.
Last edited by Ankit75 on 08 Oct 2018, 07:25, edited 1 time in total.
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Re: A circle circumscribes the triangle ABC  [#permalink]

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New post 08 Oct 2018, 07:11
OA: C

\(17^2=8^2+15^2\)

Triangle ABC is right angled triangle with Side with dimension \(17\) as hypotenuse and diameter of the circle.

Radius \(= \frac{17}{2} = 8.5\) cm
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Re: A circle circumscribes the triangle ABC  [#permalink]

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New post 08 Oct 2018, 07:42
nitesh50 wrote:
A circle circumscribes the triangle ABC and length of the three sides of the triangle are 8 cm, 15 cm and 17 cm respectively.

Find out the radius of the circle.



A.4.5
B.7.5
C.8.5
D.10.5
E.Cannot be determined

Since this is a Right Angled Triangle, area of the Triangle is 8*15/2 = 60

Radius of Circumscribed Circle = \(\frac{abc}{4A}\)

Or, Radius of Circumscribed Circle = \(\frac{8*15*17}{4*60}\)

So, Or, Radius of Circumscribed Circle = \(8.50\), Answer must be (C)

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Re: A circle circumscribes the triangle ABC   [#permalink] 08 Oct 2018, 07:42
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