A circle touches all the four sides of a quadrilateral ABCD. If AB=9~\text{cm}, BC=8~\text{cm} and CD=12~\text{cm}, then what is DA equal to?

Explanation

For a quadrilateral circumscribing a circle, the sum of lengths of opposite sides is equal: AB + CD = BC + DA. Plugging in the values gives 9 + 12 = 8 + DA \implies 21 = 8 + DA \implies DA = 13~\text{cm}.

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