दिए हुए बिन्दुओ से जाने वाली रेखा का समीकरण,
`y-a sin alpha =(a ( sin beta - sin alpha ))/(a( cos beta - cos alpha ))(x-a cos alpha )`
`=-(cos (1)/(2)(alpha + beta ))/(sin (1)/(2)(alpha + beta))(x-a cos alpha ) `
`therefore y sin (1)/(2) (alpha +beta)+x cos (1)/(2) (alpha + beta )- a sin (1)/(2) (alpha + beta )- a cos alpha cos (1)/(2)(alpha + beta )=0`
या `x cos (1)/(2) (alpha + beta )+y sin (1)/(2)(alpha + beta )-a cos (alpha -(alpha+beta)/(2))=0`
या `x cos (1)/(2)(alpha +beta) + y sin (1)/(2)(alpha+beta)-a cos ((alpha - beta)/(2))=0`
बिन्दु (0 ,0 ) से इस रेखा पर लम्ब की लम्बाई ,
`p=(a cos (1)/(2)(alpha - beta ))/(sqrt(cos^(2)(alpha+beta)/(2)+sin ^(2)(alpha+beta)/(2))`
या `(p)/(a)=cos (1)/(2)(alpha - beta)`
