Question

2. ABC is an acute-angled triangle and AD is perpendicular to BC. Prove that
2 = 2+2 −2.

Answer 1

Answer:

inΔADC-

AC²=AD²+DC²(pythagoras theorem)...................1

in ΔADB-

AB²=AD²+BD²(samee reason).............................2

AC²=AD²+(BC-BD)² (BD+DC=BC) from 1

AC²=AD²+BC²+BD²-2·BC·BD [(a-b)²=a²+b²-2ab]

AC²=(AD²+BD²)+BC²-2·BC·BD

from 2

AC²=AB²+BC²-2.BC.BD

hence proved