AP EAMCET Engineering 26 Apr 2017 Shift 1 Paper

It is given that α,β,γ are the lengths of tangents from vertices of a triangle to its incircle semi perimeter of ΔABC.
Consider the figure shown below.So,
S=α+β+γ
And,
Area of Δ‌ABC=√s(s−a)(s−b)(s−c)
=√(α+β+γ)(α)(β)(γ)
Also,
r=

Δ

s

=

√(α+β+γ)(α)(β)(γ)

α+β+γ

r2=

(α+β+γ)(α)(β)(γ)

(α+β+γ)2

(α+β+γ)2=

(α+β+γ)(α)(β)(γ)

r2

Solve further,
α+β+γ=

αβγ

r2