a Looking at the diagram, we see that BA is a common tangent to the circles D and E. Therefore, the angles formed by the radii of the circles and the segment are 90^(∘).
We know that CE∥ BA, and DB and EA are perpendicular to BA. Using the Theorem 3-9, CB ∥ EA.
Theorem 3-9
In a plane, if two lines are perpendicular to the same line, then they are parallel to each other.
Since the quadrilateral ABCE has two pairs of parallel sides, it is a parallelogram.
Recall that in a parallelogram, the opposite angles are congruent. Therefore, it is a parallelogram with four right angles, which is also called as a rectangle.
b In Part A we determined that the quadrilateral ABCE is a rectangle, meaning its opposite sides are congruent.
The length of CE is the same as the length of BA. It is 35 inches.
c Let's start by drawing the segment that joins the centers of the circles.
We see that △ DCE is a right triangle with legs of 6 and 35 inches. Using the Pythagorean Theorem, we can find the length of DE, which is also the distance between the centers of the pulleys.
