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# What is the radius of the circle above with center O?

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Math Expert
Joined: 02 Sep 2009
Posts: 55640
What is the radius of the circle above with center O?  [#permalink]

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11 Sep 2018, 02:36
00:00

Difficulty:

45% (medium)

Question Stats:

52% (01:01) correct 48% (00:59) wrong based on 38 sessions

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What is the radius of the circle above with center O?

(1) The area of the triangle shown is 10 square units.
(2) The length of PR is equal to that of QR.

Attachment:

image003.gif [ 1.83 KiB | Viewed 495 times ]

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Re: What is the radius of the circle above with center O?  [#permalink]

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11 Sep 2018, 06:19
Bunuel wrote:

What is the radius of the circle above with center O?

(1) The area of the triangle shown is 10 square units.
(2) The length of PR is equal to that of QR.

Attachment:
image003.gif

Since O is the center of the circle, triangle PQR is a right angled triangle.
with Angle PRQ=90 degrees.

Statement 1:The area of the triangle shown is 10 square units.
Area= (1/2)*Base*Height.
2 unknowns, single variable.
Insufficient.

Statement 2: The length of PR is equal to that of QR.
Bu we dont have length with us to calculate.
Insufficient

Combining Statements 1 &2:
PR=QR
therefor RO will be perpendicular to PQ and will be equal to radius of circle.
we can calculate radius from area of triangle.
Suficient.

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Re: What is the radius of the circle above with center O?  [#permalink]

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12 Sep 2018, 05:17
Bunuel wrote:

What is the radius of the circle above with center O?

(1) The area of the triangle shown is 10 square units.
(2) The length of PR is equal to that of QR.

Attachment:
image003.gif

Question : What is the radius of the circle above with center O?

Property: Triangle drwan in a semicircle with two points on diameter and third on circumference is always a right angle triangle with right angle at the circumference

Statement 1: The area of the triangle shown is 10 square units.

The height is still unknown hence the radius of the triangle can not be calculated

NOT SUFFICIENT

Statement 2: The length of PR is equal to that of QR.

i.e. Triangle is isosceles but no actual dimension of area/perimeter/side is given to calculate teh radius of the circl ehence

NOT SUFFICIENT

Combining the two statements

Area of isosceles triangle for given triangle $$= (1/2)(2r)*(r) = 10$$
where 2r is the diameter used as base and r is the height i.e. distance from O to R
Now, we can calculate r hence

SUFFICIENT

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Re: What is the radius of the circle above with center O?   [#permalink] 12 Sep 2018, 05:17
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