Open Middle®
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.
Hint
How can we figure out which central angles are or are not worth checking?
Answer
There are five potential answers:
Central angle: 104°
Inscribed angle: 52°
Circumscribed angle: 76°
Central angle: 104°
Inscribed angle: 52°
Circumscribed angle: 76°
Central angle: 106°
Inscribed angle: 53°
Circumscribed angle: 74°
Central angle: 108°
Inscribed angle: 54°
Circumscribed angle: 72°
Central angle: 138°
Inscribed angle: 69°
Circumscribed angle: 42°
Central angle: 156°
Inscribed angle: 78°
Circumscribed angle: 24°
Source: Robert Kaplinsky