# length of the tangent

A Circle is inscribed in a triangle $ABC$, where $AB=10 cm$, $BC=9 cm$ and $AC=7 cm$ . $X$, $Y$, $Z$ are points of contact of the sides $AC$, $BC$ and $AB$ with the circle respectively. $BZ=?$

In the first look, question looked simple to me. But I am not able to get to the answer. I found the In-radius using $rs = \sqrt{s(s-a)(s-b)(s-c)}$. But that is not helping me to find the required length.

In the above formula,
s=(a+b+c)/2
a,b,c -> Lengths of the sides of triangle


I would be glad to see the answer of this question. Any Hints or answers are welcome. Thanks.

Sandy

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The equations are easy to solve, but let's make it nicer. Let $BZ=p$, $CX=q$, $AZ=r$. Then $p+q+r=(10+9+7)/2=s$ (half-perimeter). So $p=s-b=13-7$. Note the appearance of the term $s-b$, which will remind you of Heron's Formula. –  André Nicolas Jul 21 '12 at 17:24