handouts/Problems/problems/geometry.tex

\problemdef{Geometry}{1}{
	\statement{
		What is the largest number of obtuse angles that nine rays emanating from one point can form on a plane?
	}

	\answer{27}
}

\problemdef{Geometry}{2}{
	\statement{
		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.
	}

	\answer{$70^\circ$}
}

\problemdef{Geometry}{3}{
	\statement{
		In a cyclic quadrilateral $ABCD$ angle $ABD$ is $30^\circ$ and angle $BCA$ is $42^\circ$. Find angle $DAB$.
	}

	\answer{$108^\circ$}
}

\problemdef{Geometry}{4}{
	\statement{
		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 $AB$.
	}

	\answer{12}
}

\problemdef{Geometry}{5}{
	\statement{
		What is the largest number of sides a polygon that is the intersection of a quadrilateral and a triangle can have?
	}

	\answer{8}
}