Question

The sum of the lengths of two opposite sides of the circumscribed quadrilateral is 10 cm, and its area is 12 cm2. Find the radius of the inscribed circle.

Answer 1

Answer:

1.2 cm

Step-by-step explanation:

The area of sircumscribed quadrilateral over a circle is equal to

$A=s\cdot r,$

where s is semi-perimeter of the quadrilateral and r is the radius of the circle.

Use property of circumscribed quadrilateral: The sums of the opposite sides are equal.  

So, if the sum of two opposite sides of the circumscribed quadrilateral is 10 cm, then the sum of another two sides is also 10 cm and the perimeter of the quadrilateral is 20 cm. Hence,

$s=\dfrac{20}{2}=10\ cm$

Now,

$A=s\cdot r\\ \\12=10r\\ \\r=\dfrac{12}{10}=1.2\ cm$