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# Task 4 - 120924 

A convex tangential quadrilateral $A B C D$ (a quadrilateral in which a circle can be inscribed such that it touches each of the four sides of the quadrilateral at one point) has the perimeter $u$, and the radius of its incircle is $r$.

Calculate the area $F$ of this tangential quadrilateral!
Let $M$ be the center and $r$ the radius of the incircle. Then the tangential quadrilateral is divided into four sub-triangles $A B M, B C M, C D M, A D M$, such that the height of the triangles on the outer edge is precisely the inradius. Therefore, for the area, we have:

$$
F=\frac{a r}{2}+\frac{b r}{2}+\frac{c r}{2}+\frac{d r}{2}=\frac{u r}{2}
$$

### 6.14.3 III. Level 1972, Class 9