Question

in angle abc ab is equals to BC is equals to see a and Angle B is equals to anger over a prove that a bisects angle C A B​

Answer 1

Answer:

In △ABC, AD bisects ∠A

∴    

AB

AC

​

=

BD

DC

​

⇒  

c

b

​

=

BD

DC

​

⇒  

c

b

​

+1=

BD

DC

​

+1         [ Adding 1 to both sides ]

⇒  

c

b+c

​

=

BD

DC+BD

​

⇒  

c

b+c

​

=

BD

BC

​

       [ DC+BD=BC ]

⇒  

c

b+c

​

=

BD

a

​

∴   BD=

b+c

ac

​

         [ Hence proved ]

Similarly since AD bisects ∠A.

∴  

AC

AB

​

=

DC

BD

​

⇒  

b

c

​

=

DC

BD

​

⇒  

b

c

​

+1=

DC

BD

​

+1

⇒  

b

c+b

​

=

DC

BD+DC

​

⇒  

b

c+b

​

=

DC

BC

​

⇒  

b

c+b

​

=

DC

a

​

∴   DC=

b+c

ab

​

           [ Hence proved ]

Step-by-step explanation: