31 lines
801 B
TeX
31 lines
801 B
TeX
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\problemdef{Geometry}{1}{
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\statement{
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What is the largest number of obtuse angles that nine rays emanating from one point can form on a plane?
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}
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\answer{27}
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}
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\problemdef{Geometry}{2}{
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\statement{
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The three sides of the trapezoid are equal, and one of the angles is $40^\circ$ larger than the other. Find an acute angle between the diagonals of the trapezoid.
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}
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\answer{$70^\circ$}
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}
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\problemdef{Geometry}{3}{
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\statement{
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In a cyclic quadrilateral $ABCD$ angle $ABD$ is $30^\circ$ and angle $BCA$ is $42^\circ$. Find angle $DAB$.
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}
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\answer{$108^\circ$}
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}
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\problemdef{Geometry}{4}{
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\statement{
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In a triangle $ABC$, angle $B$ is $20^\circ$, and angle $C$ is $40^\circ$. The bisector $AD$ of angle $A$ is 12. Find the difference between the sides $BC$ and $AB$.
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}
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\answer{12}
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}
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