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 Author: burnttwinky [ 19 Jan 2010, 21:04 ] Post subject: In triangle ABC, point X is the midpoint of side AC and In triangle ABC, point X is the midpoint of side AC and point Y is the midpoint of side BC. If point R is the midpoint of line segment XC and if point S is the midpoint of line segment YC, what is the area of triangular region RCS ? (1) The area of triangular region ABX is 32. (2) The length of one of the altitudes of triangle ABC is 8.OPEN DISCUSSION OF THIS QUESTION IS HERE: in-triangle-abc-point-x-is-the-midpoint-of-side-ac-and-82671.html

Author:  gurpreetsingh [ 19 Jan 2010, 21:27 ]
Post subject:  Re: OG #12 Problem 109

IMO ans should be A.

Area of triangle ABX = area of BXC as median divides the triangle into 2 equal areas.

similarly area of XYC = 1/2 BXC = ( 1/2 ABX) = 1/2 * 32 = 16

Now XYC and RSC are similar triangles
Since we have area of XYC , we can find the area of triangle RSC.
Thus statement 1 is sufficient.

Statement 2 seems not sufficient, not enough parameters given.