Point P is 9 units from the center of a circle of radius 15.
How many different chords of the circle contain P and have integer lengths?
(15-9) * (15+9) = 6 * 24 = 144
144=24⋅32
144=(2⋅3)⋅(23⋅3)=6⋅24144=(23)⋅(2⋅32)=8⋅18144=(32)⋅(24)=9⋅16144=(22⋅3)⋅(22⋅3)=12⋅12
1. chord ( length = 30 = 6+24 )
2. chord ( length = 26 = 8+18 )
3. chord ( length = 26 = 18+8 )
4. chord ( length = 25 = 9+16 )
5. chord ( length = 25 = 16+9 )
6. chord ( length = 24 = 12+12 )
see chord theorem:

