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Vithal
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In GMAT, does quadrilateral always mean cyclic 08 Jun 2005, 23:34
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In GMAT, does quadrilateral always mean cyclic quadrilateral? (sum of internal angles = 360 ?)



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In GMAT, does quadrilateral always mean cyclic 09 Jun 2005, 09:34
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Vithal
In GMAT, does quadrilateral always mean cyclic quadrilateral? (sum of internal angles = 360 ?)
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A convex quadrilateral has the sum of internal angels as 360

A cyclic quadrilateral , the opp angles are supplementary.

HMTG.
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In GMAT, does quadrilateral always mean cyclic 09 Jun 2005, 22:43
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Hmmm I didn't know the term so I googled it.

A cyclic quadrilateral is a quadrilateral for which a circle can be circumscribed so that it touches each polygon vertex.
The area of a cyclic quadrilateral is the maximum possible for any quadrilateral with the given side lengths. The opposite angles of a cyclic quadrilateral sum to Pi radians.

I don't think we can assume all quadrilaterals in GMAT are cyclic quadrilaterals.
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In GMAT, does quadrilateral always mean cyclic 09 Jun 2005, 22:53
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Hmmm I didn't know the term so I googled it.

A cyclic quadrilateral is a quadrilateral for which a circle can be circumscribed so that it touches each polygon vertex.
The area of a cyclic quadrilateral is the maximum possible for any quadrilateral with the given side lengths. The opposite angles of a cyclic quadrilateral sum to Pi radians.

I don't think we can assume all quadrilaterals in GMAT are cyclic quadrilaterals.
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They say explicitly in OG 10 math section that they use only convex polygons, so that the sum of their angles can be calculated using (n-2)180

convex means that for any two points on or inside the polygon, the line that connects them will belong to that polygon.
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In GMAT, does quadrilateral always mean cyclic 09 Jun 2005, 22:55
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I agree that they only use convex polygons. But not all convex polygons are cyclic quadrilateral right? You could draw a cyclic quadrilateral with all its points in a circle, and then lower one of the vertex so that it is not on a circle and it still can be convex.
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In GMAT, does quadrilateral always mean cyclic 09 Jun 2005, 23:00
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I agree that they only use convex polygons. But not all convex polygons are cyclic quadrilateral right? You could draw a cyclic quadrilateral with all its points in a circle, and then lower one of the vertex so that it is not on a circle and it still can be convex.
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Oh yeah, sure. I was just refering to Vithal definition of cyclic - he said that the sum of its angles needs to equal 360.



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