Question

3) in SABC.M.CABC = 90%, seg BN i seg AC, AN 9,NC 16 then ſind BN.​

Answer 1

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We have XY Il AC (Given) ZBXY=ZA and ZBYX=ZC (Corresponding angles) Terefore, A ABC ~ A XBY (AA similarity criterion) 2 & ar (ABC) _ (=) (Theorem 6.6) (1) ar (XBY) XB ‘* ar (ABC) = 2 ar (XBY) (Given) h ar (ABC) 2 (2) ar (XBY) " 1 "eco, from (1) and (2), AB 2 2 ie AB _ v2 -|=* xB 1 (se) 7a XB AB 2 1

XB al

SAB 2 Jjz-!1 2-¥2. AX = ABXB VO=-! is. a ;

Answer 2

We have XY Il AC (Given) ZBXY=ZA and ZBYX=ZC (Corresponding angles) Terefore, A ABC ~ A XBY (AA similarity criterion) 2 & ar (ABC) _ (=) (Theorem 6.6) (1) ar (XBY) XB ‘* ar (ABC) = 2 ar (XBY) (Given) h ar (ABC) 2 (2) ar (XBY) " 1 "eco, from (1) and (2), AB 2 2 ie AB _ v2 -|=* xB 1 (se) 7a XB AB 2 1

XB al

SAB 2 Jjz-!1 2-¥2. AX = ABXB VO=-! is. a ;

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