# RT - inscribed circle

In a rectangular triangle has sides lengths> a = 30cm, b = 12.5cm. The right angle is at the vertex C. Calculate the radius of the inscribed circle.

Result

r =  5 cm

#### Solution:

$a=30 \ \text{cm} \ \\ b=12.5 \ \text{cm} \ \\ \ \\ c=\sqrt{ a^2+b^2 }=\sqrt{ 30^2+12.5^2 }=\dfrac{ 65 }{ 2 }=32.5 \ \text{cm} \ \\ \ \\ S=\dfrac{ a \cdot \ b }{ 2 }=\dfrac{ 30 \cdot \ 12.5 }{ 2 }=\dfrac{ 375 }{ 2 }=187.5 \ \text{cm}^2 \ \\ s=(a+b+c)/2=(30+12.5+32.5)/2=\dfrac{ 75 }{ 2 }=37.5 \ \text{cm} \ \\ \ \\ r=S/s=187.5/37.5=5 \ \text{cm}$

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