High School: Geometry

Directions: Using the digits 0 to 9 at most one time each, place a digit in each box so that the central angle has the greatest possible value. Source: Robert Kaplinsky

Directions: Using the digits 0 to 9 at most one time each, place a digit in each box two times: once where the central angle is greater than 130° and once where it is less than 130°. You may reuse all the digits each time. Source: Robert Kaplinsky

Directions: Using the digits 0 to 9 at most one time each, place a digit in each box so that the radius and angle measure result in the sector area is as close to 60 units2 as possible. Source: Robert Kaplinsky

Directions: Using the digits 0 to 9 at most one time each, place a digit in each box so that the radius and angle measure result in the sector area. Source: Robert Kaplinsky

Directions: Using exactly five geometric markings to show that a quadrilateral is a square. Source: Robert Kaplinsky

Directions: Using the integers -9 to 9 at most one time each, fill in the boxes to create coordinates that represent the vertices of the triangle with the smallest possible area. Source: Robert Kaplinsky

Directions: Using the integers -9 to 9 at most one time each, fill in the boxes to create coordinates that represent the vertices of two triangles: one with an area of less than 55 units2 and one with an area of more than 55 units2. You may reuse all the integers each time. Source: Robert Kaplinsky

Directions: Using the digits 0 to 9 at most one time each, fill in the boxes to create two perpendicular lines whose solution is as close to the origin as possible. Source: Robert Kaplinsky

Directions: Using the digits 0 to 9 at most one time each, fill in the boxes to create two perpendicular lines. Source: Robert Kaplinsky

Directions: Using the digits 1 to 9 at most two times each, place a digit in each box to make a circle with the least possible area. Source: Robert Kaplinsky