Question

AABC is an obtuse angle, obtuse angled at B. If AD I CB , prove that
AC2 = AB2 + BC2 + 2BC.BD
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Answer 1

Answer:

Given: ABC is obtuse triangle.

AB² = AD² + DB² ⟶ (1)

AC² = AD² + DC² ⟶ (2)

from (1) AD² = AB − DB²

∴AC² = AB² − DB² + (DB + BC)²

[∵BC = DB + BC]

AC² = AB² − DB² + DB² + BC² + 2BC × DB

AC² = AB² + BC² + 2BC × DB

Hence Proved...!