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tmua.me Extreme Set B Paper 1 · Q7

Paper 1Geometry

The positive real numbers a,b,ca,b,c satisfy a≤b≤ca\le b\le c. Both

a, b, cand1a, 1b, 1ca,\ b,\ c \qquad\text{and}\qquad \frac1a,\ \frac1b,\ \frac1c

can be used as the side lengths of triangles of positive area.

Writing R=c/aR=c/a, which of the following is the complete set of possible values of RR?

A1≤R<21\le R<2
B1≤R≤3+521\le R\le\dfrac{3+\sqrt5}{2}
C1≤R<3+521\le R<\dfrac{3+\sqrt5}{2}
D1<R<3+521<R<\dfrac{3+\sqrt5}{2}
E1≤R<1+21\le R<1+\sqrt2
F1≤R<1+521\le R<\dfrac{1+\sqrt5}{2}

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