In the gure below, arc SBT is one quarter of a circle with center R and radius
r. The length plus the width of rectangle ABCR is 8, and the perimeter of the shaded region
is 10 + 3. Find the value of r. Answers:
A) 6
B) 6:25
C) 6:5
D) 6:75
E) 7
Set x = RC and y = AR. It must then be x+y = 8 (by hypothesis) and x2+y2 = r2   (since the rectangle ABCR has one vertex in the circle). The perimeter of the shaded area is   then AS + SBT + TC + AC = (r 􀀀 y) + r=2 + (r 􀀀 x) +   p   x2 + y2 = 3r + r=2 􀀀 (x + y) =   3r + r=2 􀀀 8. All we need to so is solve for r in the equation 18 + 3 = (3 +   2 )r.   correct answer 6
<result>A</result>
In the gure below, arc SBT is one quarter of a circle with center R and radius
r. The length plus the width of rectangle ABCR is 8, and the perimeter of the shaded region
is 10 + 3. Find the value of r.