Question

In triangle ABC angle ACB is an obtuse angle. Seg AD is perpendicular to line BC then prove that AB^2= BC^2 +AC^2+2BC×CD



STD X model question paper
pg 518

Answer 1

in triangle ADB
angle ADB is equal to 90 degree
a b square is equal to ad square + BD square as per phythogrus theorem
eq1...
in triangle abc
angle abc is equal to 90 degree
AC square is equal to ad square + dc square
eq2....
from eq1
a b square is equal to 80 square + BC + CD the whole square
which is equal to a b square + b square + BC square + c b square + 2 *DC *CB

=a b squared equal to bc sq+ac sq+2*dc*cd
(from eq 2 where ac sq=dc sq +ac sq)