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
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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:
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