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Euclid Sample Paper 2 · Q10

Paper 2Logic & proofGeometry

The positive real numbers

a<b<ca<b<c

are the side lengths of a non-degenerate triangle. Define

x=b+c−a,y=c+a−b,z=a+b−c.x=b+c-a,\qquad y=c+a-b,\qquad z=a+b-c.

Which statements must be true?

  • I. z<y<xz<y<x.
  • II. x,y,zx,y,z are necessarily the side lengths of a non-degenerate triangle.
  • III. x+y+z=a+b+cx+y+z=a+b+c.
Anone
BI only
CII only
DIII only
EI and II only
FI and III only
GII and III only
HI, II and III

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