



 
Laura, Use the theorem that the lengths of the two tangents from a point outside a circle are equal (measured from the outside point to the point of tangency. In fact, you use the theorem three times. Label the point T where XY is tangent the circle. In your problem you have two tangents to your circle from X: XT is a portion of XY and XA a portion of the tangent CA. Those tangents have the same length  that is, XA = XY. Similarly, you have two tangents from Y. The length of the line XY equals the sum of those two tangents (XT + TY). Now write the perimeter, namely CX + XY + YC, using those other pieces, namely XA and YB, in place of XY. Chris  


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