A circle is inscribed in a $A B C$ having sides $A B = 8$ $c m$ , $B C = 10$ $c m$ and $A C = 12$ $c m$ . (see figure.). Find $A D$ , $B E$ and $C F$ .

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Solution

$(x^{2} - 3 x + 4) (x^{2} + 2 x + 5)$
Let $α, β$ be roots of $1^{s t}$ quadratic and
$γ, δ$ be roots of $2^{n d}$ quadratic
$α + β = \frac{(-) (- 3)}{1}; γ + δ = \frac{- 2}{1}; α + β + γ + δ = 1 - (- b / a)$
$α β = \frac{4}{1}; γ δ = \frac{5}{1}; α β γ δ = 20 = (d / a)$
$∴$ equation will be $x^{2} - x + 20 = 0$

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A circle is inscribed in a ABC having sides AB=8 cm , BC=10 cm and AC=12 cm . (see figure.). Find AD, BE and CF .

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A circle is inscribed in a $A B C$ having sides $A B = 8$ $c m$ , $B C = 10$ $c m$ and $A C = 12$ $c m$ . (see figure.). Find $A D$ , $B E$ and $C F$ .