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# What is the area of the triangle PQR?

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Math Expert
Joined: 02 Sep 2009
Posts: 55277
What is the area of the triangle PQR?  [#permalink]

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14 Sep 2018, 01:41
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Difficulty:

65% (hard)

Question Stats:

55% (01:34) correct 45% (01:29) wrong based on 22 sessions

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What is the area of the triangle PQR?

(1) The radius of the circle is 5
(2) c = 1

Attachment:

image006.jpg [ 5.39 KiB | Viewed 604 times ]

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Re: What is the area of the triangle PQR?  [#permalink]

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14 Sep 2018, 01:59
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Joined: 31 Jul 2017
Posts: 516
Location: Malaysia
GMAT 1: 700 Q50 V33
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WE: Consulting (Energy and Utilities)
What is the area of the triangle PQR?  [#permalink]

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Updated on: 14 Sep 2018, 02:20
Bunuel wrote:

What is the area of the triangle PQR?

(1) The radius of the circle is 5
(2) c = 1

Attachment:
image006.jpg

I feel, it should be C.

Statement I:

$$a+c = 10$$, but nothing about b. Hence, Insufficient

Statement II:

$$c =1$$, but nothing about a, b. Hence, Insufficient.

Combined:

$$a =9, c= 1$$

$$b^2 = 5^2 - 4^2, b = 3$$

Hence, C.
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Originally posted by rahul16singh28 on 14 Sep 2018, 02:09.
Last edited by rahul16singh28 on 14 Sep 2018, 02:20, edited 1 time in total.
Math Expert
Joined: 02 Aug 2009
Posts: 7688
What is the area of the triangle PQR?  [#permalink]

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14 Sep 2018, 02:16
1
Bunuel wrote:

What is the area of the triangle PQR?

(1) The radius of the circle is 5
(2) c = 1

Attachment:
The attachment image006.jpg is no longer available

rahulkashyap
The two things we require is the diameter and the place of point Q..
If you have these, you will be able to make a unique ∆PQR..
Now combined..
Radius is 5, so a unique circle...a+c=10
c is 1, so unique place of Q. And thus unique triangle.
So we should be able to get the area..

If it were a PS..
Join centre say O with Q..
So ∆OQS, S is the point on PR where altitude from Q drops..
OS=5-c=5-1=4
So QS=√(5^2-4^2)=√9=3

So area =1/2*3*10=15

C
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PicsArt_09-14-02.52.20.jpg [ 8.84 KiB | Viewed 464 times ]

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What is the area of the triangle PQR?   [#permalink] 14 Sep 2018, 02:16
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