dtweah wrote:A circle is inscribed in quadrilateral ABCD where the circle is tangent to each side of the quadrilateral , with AB = 16 and CD = 10. What is the perimeter of the quadrilateral?
(a) 50
(b) 52
(c) 54
(d) 56
(e) 58
If the circle touches the sides AB, BC, CD, and DA in P, Q, R, and S, respectively, then let DR = DS = x such that CR = CQ = 10 - x, and let BP = BQ = y such that AP = AS = 16 - y.
Now, AD + BC = (AS + DS) + (BQ + CQ) = (16 - y + x) + (y + 10 - x) = 26
Hence, the perimeter = AB + CD + AD + BC = 16 + 10 + 26 = [spoiler]
52[/spoiler].
[spoiler]
B[/spoiler]
