• Calculons IN² et PI² + PN²
[tex] {in}^{2} = {io}^{2} + {on}^{2} \\ \: \: \: \: \: \: \: = {io}^{2} + {(ob - bn)}^{2} \\ \: \: \: \: \: \: \: = \: {12}^{2} + {(12 - 3)}^{2} \\ {in}^{2} = 225[/tex]
PI² + PN² = [tex]{pi}^{2} + {( {pb}^{2} + {bn}^{2} )}^{2}\\ = {pi}^{2} + {( {(sb - sp)}^{2} + {bn}^{2} )}^{2} \\ = {pi}^{2} + {( {(sb -\sqrt{( {pi}^{2} - {si}^{2})})}^{2} + {bn}^{2} )}^{2} \\ = {13}^{2} + {( {(12 -\sqrt{( {13}^{2} - {12}^{2})})}^{2} + {3}^{2} )}^{2} \\ = 169 + ({(12 -\sqrt{(169 - 144)})}^{2} + 9) \\ = 169 + ({7}^{2} + 9) \\ = 169 + 49 + 9 \\ = 227[/tex]
