11. Reasoning Given: Quadrilateral WXYZ is circumscribed about circle A. Prove: WX+ YZ=XY+ WZ W

X, Y, and Z are on circle O such that mXY=120, mYZ=130, and mXZ=110. Suppose that triangle XYZ is drawn and that the triangle ABC is constructed with its sides tangent to circle O at X, Y, and Z. Are XYZ and ABC similar triangles?

In the drawing, suppose that ZX is the perpendicular bisector of WY. What type of quadrilateral is WXYZ?

Prove: In a circle containing two unequal chords, the longer chord corresponds to the larger central angle. HINT: You may use any theorems stated in this section.

The center of a circle of radius 2 inches is at a distance of 10 inches from the center of a circle of radius length 3 inches. To the nearest tenth of an inch, what is the approximate length of a common internal tangent? Use the hint provided in Exercise 38. HINT: use similar triangles to find OD and DP. Then apply the Pythagorean Theorem twice.

Generalize your findings in Exercise 33. 33. Can you use the construction for the midpoint of a segment to divide a line segment into a three congruent parts? c six congruent parts? b four congruent parts? d eight congruent parts?