Geometry

This topic has expert replies
Legendary Member
Posts: 869
Joined: Wed Aug 26, 2009 3:49 pm
Location: California
Thanked: 13 times
Followed by:3 members

Geometry

by heshamelaziry » Tue Oct 27, 2009 9:58 pm
Q. The diameter of a circle is D and the area is A . If the given the circle is inscribed in a rectangle, what is the area of the circle?

1] The diagonal of the rectangle is 12 cm
2] The area of the rectangle is 62 cm^2

[spoiler]the answer says this: Given : circle is inscribed in a rectangle , So it is a square. i.e. diameter of circle = side of square.

1) diagonal is 12 cm so side = 12 / sqrt(2), so area of circle can be found. Sufficient
2) area is 62, so side = sqrt(62), so area of circle can be found. Sufficient [/spoiler]


How can he deduce the bold part? a square is not a rectangle ?
Source: — Data Sufficiency |

Newbie | Next Rank: 10 Posts
Posts: 4
Joined: Sun Oct 25, 2009 10:12 pm

Circle Inscribed in Rectangle

by siddogg » Wed Oct 28, 2009 12:24 am
The key to this question is in the wording of the problem. It says that the circle is INSCRIBED inside a rectangle. When a circle is incribed in a rectangle, it implies that 4 points equidistant from each other all touch the rectangle. The only way this is true is if in fact the rectangle is a square.

Draw a circle, then draw a box around it and make sure it touches the circle in 4 different places, the only box you can successfully draw is a circle.

Rule:
All Squares are ALSO rectangles
Some rectangle are sqaures, but not all obviously

Answer is D, both sufficient