# Cathethus and the inscribed circle

In a right triangle is given one cathethus long 14 cm and the radius of the inscribed circle of 5 cm. Calculate the area of this right triangle.

Result

S =  157.5 cm2

#### Solution:

$b = \dfrac{ 2r(a-r)}{a-2r} = \dfrac{ 2\cdot 5(14-5)}{ 14-2 \cdot 5} = 22.5 \ cm \ \\ S = ab/2 = 14 \cdot 22.5 /2 = 157.5 \ cm^2$

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