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