Question

In triangle ABC a,b,c are the sides. r1 is exradius opposite to A and ha is the length of altitude through A. Prove that a/(b+c) = r1/(ha+r1)​

Answer 1

Answer:

r⋅r

1

⋅r

2

⋅r

3

=

s

△

×

s−a

△

×

s−b

△

×

s−c

△

⇒

s(s−a)(s−b)(s−c)

△

4

[r=

s

△

,r

1

=

s−a

make me brilliant

△

,r

2

=

s−b

△

,r

3

=

s−c

△

]

r⋅r

1

⋅r

2

⋅r

3

=

△

2

△

4

=△

2

Hence, 2△ is the correct answer.