CAT 2024 Geometry & Mensuration Question (Medium)

Question

The midpoints of sides AB, BC, and AC in ABC are M, N, and P, respectively. The medians drawn from A, B, and C intersect the line segments MP, MN and NP at X, Y, and Z, respectively. If the area of ABC is 1440 sq cm, then the area, in sq cm, of XYZ is

Accepted Answer

Step 1 Compare triangles and , , so is parallel to By midpoint theorem, So, ! Triangle ABC and MNP https optima-learn.b-cdn.net quantPyqImages img_1751026298512_28.jpg Step 2 Now compare triangles and , , so is parallel to Again using midpoint theorem, So, ! Triangle MNP and XYZ https optima-learn.b

CAT 2024

Quantitative

Geometry & Mensuration

Medium

The midpoints of sides AB, BC, and AC in △ ABC are M, N, and P, respectively. The medians drawn from A, B, and C intersect the line segments MP, MN and NP at X, Y, and Z, respectively. If the area of △ ABC is 1440 sq cm, then the area, in sq cm, of △ XYZ is

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