SajjadAhmad wrote:

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°.

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.

_________________

David

Senior tutor at examPAL

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