Question

please answer the 16 one fast

Answer 1

if AD² = BD x CD
then, AD/BD= CD/AD
 ΔABD ≈ ΔABC
∠D = ∠D
∠ABD= ∠BAC
from ΔABD
 AB² = AD²+BD²                          - (1)
fromΔACD
AC² = AD² + CD²                        -(2)
From 1 and 2
AB² +AC² =AD²+ BD²+AD²+CD²
AB²+AC²= 2AD²+BD²+CD²
AB²+AC²= BD²+ CD²
AB²+AC²= BC²
proved