Chapter 6 - Section 6.3 - Line and Segment Relationships in the Circle - Exercises - Page 308: 36

$TM = 1.17$

Since the hypotenuse of a right isosceles triangle is $\sqrt{4}$ more than a leg, we obtain that the hypotenuse is $4\sqrt2$ and that the legs are each 4. Since MT and NT are both the radius of the circle, we see that they are equals. Thus, we find: $ MT + TN + RM + NS = 8 \\ x + x + y + y = 8 \\ x+ y = 4$ We know that $2 \sqrt2$ since it is half of the hypotenuse of the larger triangle, so we find: $ y = TM = 4 - 2\sqrt2 = 1.17$