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21 Dec 2017, 03:33
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
40% (01:05) correct
60%
(00:49)
wrong
based on 55
sessions
History
Date
Time
Result
Not Attempted Yet
Can a circle be drawn so that its circumference includes all four vertices of quadrilateral Q ?
(1) All four sides of Q are equal in length.
(2) Each of the interior angles of Q measures 90°.
(1) All four sides of Q are equal in length.
(2) Each of the interior angles of Q measures 90°.
21 Dec 2017, 06:39
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SajjadAhmad
Question: Can a circle inscribe a given Quadrilateral?
Statement 1: All four sides of Q are equal in length.
Case 1: In case of square, the answer to question is YES
Case 2: In case of all other Rhombus, the answer to question is NO
NOT SUFFICIENT
Statement 2: Each of the interior angles of Q measures 90°.
Now the quadrilateral is definitely a rectangle (which includes the case of square as well)
Hence answer yo the question is f=definitely YES
SUFFICIENT
Answer: Option B
21 Dec 2017, 10:31
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SajjadAhmad
Since we're asked if a circle can be drawn, why not just try? This is a classic Alternative approach.
(1) All four sides of Q are equal in length so it is a square or a more messy rhombus.
We'll try drawing a square inscribed by a circle - yes!
We'll try drawing a rhombus inscribed by a circle - no!
Playing with the figure, we can SEE that this won't work because the diagonals of a rhombus aren't always equal.
Insufficient!
(2) Our quadrilateral is now a rectangle.
Once again, we'll try drawing a rectangle inscribed inside a circle.
No matter how we draw our rectangle, this works!
Therefore (2) is sufficient and we can mark (B) as our answer (even if we don't understand why!)
** Note - (2) is true because we can set the diagonals of the rectangle as the diameter of the circle and the meeting point of the diagonals as its center.
