Answer:
2(R+r)=a+b
Step-by-step explanation:
We know R=
4Δ
abc
- - - - - - - - (1)
Also r=
s
Δ
=(s−c)tan
2
C
- - - - - - - - - - 2
Given ∠C=
π
hence Δ=
b×a
--------3
put eqn(3) in eqn(1)
we get R=
4×b×c
We will get R=
c
- - - - - - 4
Now s=
a+b+c
Put it on eqn(2)
After solving eqn(2) we will get
r=
a+b−c
- - - - - - - - 5
now 2(R+r)=2(
+
)
Hence, 2(R+r)=a+b
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Answers & Comments
Answer:
2(R+r)=a+b
Step-by-step explanation:
We know R=
4Δ
abc
- - - - - - - - (1)
Also r=
s
Δ
=(s−c)tan
2
C
- - - - - - - - - - 2
Given ∠C=
2
π
hence Δ=
2
b×a
--------3
put eqn(3) in eqn(1)
we get R=
2
4×b×c
abc
We will get R=
2
c
- - - - - - 4
Now s=
2
a+b+c
Put it on eqn(2)
After solving eqn(2) we will get
r=
2
a+b−c
- - - - - - - - 5
now 2(R+r)=2(
2
c
+
2
a+b−c
)
Hence, 2(R+r)=a+b