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tmua.me Extreme Set C Paper 2 · Q4

Paper 2TrigonometryGeometry

Two squares of side length 11 have the same centre OO. One is obtained by rotating the other through an angle θ\theta, where

0<θ<π4.0<\theta<\frac\pi4.

Their common region is an octagon of area 8/98/9. The distances from OO to its eight vertices are d1,d2,…,d8d_1,d_2,\ldots,d_8.

What is the value of

d12+d22+⋯+d82 ?d_1^2+d_2^2+\cdots+d_8^2\,?

Diagram for question 4

A10481\dfrac{104}{81}
B19081\dfrac{190}{81}
C20881\dfrac{208}{81}
D21781\dfrac{217}{81}
E22681\dfrac{226}{81}
F24481\dfrac{244}{81}

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