The important question of class 10th ncert book of exercise 6.6 of triangles chapter , What is the best way to solve this problem because it is also an important question In Figure, ABC is a triangle in which ∠ABC > 90° and AD ⊥ CB produced. Prove that AC2= AB2+ BC2+ 2 BC.BD.
By applying Pythagoras Theorem in ∆ADB, we get,
AB2 = AD2 + DB2 ……………………… (i)
Again, by applying Pythagoras Theorem in ∆ACD, we get,
AC2 = AD2 + DC2
AC2 = AD2 + (DB + BC) 2
AC2 = AD2 + DB2 + BC2 + 2DB × BC
From equation (i), we can write,
AC2 = AB2 + BC2 + 2DB × BC
Hence, proved.