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655-705 (Hard)|   Geometry|      
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Kritisood
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In the given figure, O is the centre of the circle and RQ is the diago 26 Apr 2020, 11:02
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55% (hard)

Question Stats:

58% (02:02) correct 42% (01:56) wrong based on 157 sessions

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In the given figure, O is the centre of the circle and RQ is the diagonal of the quadrilateral PQRS. Find the area of PQRS.
(1) Area of triangle ORS = 30 unit sq
(2) PS is the diameter of circle with angle ROS = 90 degree
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C

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TestPrepUnlimited
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In the given figure, O is the centre of the circle and RQ is the diago 26 Apr 2020, 14:15
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Kritisood
In the given figure, O is the centre of the circle and RQ is the diagonal of the quadrilateral PQRS. Find the area of PQRS.
(1) Area of triangle ORS = 30 unit sq
(2) PS is the diameter of circle with angle ROS = 90 degree
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Note we do not know if PQRS is a square yet. We can only confirm it is a rectangle.

Statement 1:
We don't know anything about QOS, insufficient.

Statement 2:
Now we can confirm PQRS is a square. We have no lengths however so insufficient.

Combined:
The area of PQRS is 30 * 4. Sufficient.

Ans: C
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In the given figure, O is the centre of the circle and RQ is the diago 27 Apr 2020, 11:25
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Kritisood
In the given figure, O is the centre of the circle and RQ is the diagonal of the quadrilateral PQRS. Find the area of PQRS.
(1) Area of triangle ORS = 30 unit sq
(2) PS is the diameter of circle with angle ROS = 90 degree

Note we do not know if PQRS is a square yet. We can only confirm it is a rectangle.

Statement 1:
We don't know anything about QOS, insufficient.

Statement 2:
Now we can confirm PQRS is a square. We have no lengths however so insufficient.

Combined:
The area of PQRS is 30 * 4. Sufficient.

Ans: C
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Hey, how can we confirm from statement 2 that PQRS is a sq? we don't know about POQ or QOS.
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In the given figure, O is the centre of the circle and RQ is the diago 18 Aug 2022, 23:15
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In the given figure, O is the centre of the circle and RQ is the diagonal of the quadrilateral PQRS. Find the area of PQRS.

(1) Area of triangle ORS = 30 unit sq

Could be a rectangular quadrilateral, not a square. so we don't know the area of the entire quad.

(2) PS is the diameter of circle with angle ROS = 90 degree

No measure whatsoever of the rectangle or circle.

1 + 2:

Both of the lines are bisectors. The angle is 90 degrees. Meaning the opposite angle is also 90 degrees. Hence why the other remaining angles are also 90 each. Cannot be a rectangle. Only a square. SUFF.
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In the given figure, O is the centre of the circle and RQ is the diago 21 Nov 2025, 08:54
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Something's a miss, because even with both the statements we still don't know if O lies on PS.

just because ROS is 90 degrees we can't say that PQRS is a square as we don't know if O is lies on PS.

And at the end, all we need is that to know that O lies on one of the diagonals, making the the area under triangle ORS = 1/4 (area of PQRS)
Kritisood
In the given figure, O is the centre of the circle and RQ is the diagonal of the quadrilateral PQRS. Find the area of PQRS.
(1) Area of triangle ORS = 30 unit sq
(2) PS is the diameter of circle with angle ROS = 90 degree
Show more
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