Question

In a triangle ABC, if r:r1 = r2:r3then which of the following are true?
a^2 + b^2 + c^2=8R^2
sin^2 A +sin^2 B + sin^2 C = 2
a² +b² = c^2
∆=s(s-a)​

Answer 1

Step-by-step explanation:

r

1

=r

2

+r

3

+r⟹r

1

−r=r

2

+r

3

⟹sin

2

A

cos

2

B

cos

2

C

−sin

2

A

sin

2

B

sin

2

C

=sin

2

B

cos

2

A

cos

2

C

−sin

2

C

cos

2

A

cos

2

B

⟹sin

2

A

(cos

2

B

cos

2

C

−sin

2

B

sin

2

C

)=cos

2

A

(sin

2

B

cos

2

C

−sin

2

C

cos

2

B

)

⟹sin

2

A

cos

2

(B+C)

=cos

2

A

sin

2

(B+C)

⟹tan

2

A

=tan

2

(B+C)

⟹A=B+C⟹2A=180

∘

⟹A=90

∘