CPM Homework Help : INT2 Problem 12-22

Circle, with center, D, and points, a, and, c, on the circle, and point, b, outside the circle. Rays, b, a, and, b, c, create angle, A, b, c, with sides that are tangent to the circle Dennis plans to place a circular hot tub in the corner of his backyard so that it is tangent to a fence on two sides, as shown in the diagram at right. The switch to turn on the air jets is located at point $B$ .

If the length of the diameter of the hot tub is $6$ feet and $AB=4$ feet, how long does his arm need to be for him to reach the switch and still stay in the tub? (Assume that Dennis will be in the tub when he turns the air jets on and that the switch is level with the top edge of the hot tub.)

Hint:

Use the Pythagorean Theorem to find the length of $\overline{BD}$