Solve for the indicated variable.
1. Rays AB and AC are tangents. x = ?
2. Rays AB and AC are tangents. x = ?
3. Ray AB is a tangent. y = ?
4. Line k is a tangent to both circles. z = ?
5. Quadrilateral POST is circumscribed about circle Y. OR = 13 and ST = 12. What is the perimeter of POST?
6. Quadrilateral SHOW is circumscribed about circle X. WO = 14, HM = 4, SW = 11, and ST = 5. What is the perimeter of SHOW?
In exercises 7-12, use the segments below with the given lengths r, s, and t. Make a sketch of what you are trying to construct.
7. Construct a circle with radius r. Make a point on the circle. Construct a tangent through this point.
8. Construct a circle with radius t. Choose 3 points on the circle and label them X, Y, and Z. Construct a triangle that is circumscribed about the circle and tangent at the points X, Y, and Z.
9. Construct two congruent, externally tangent circles with radius s.
10. Construct a third circle that is both congruent and externally tangent to the two circles you constructed in exercise 9.
11. Construct two internally tangent circles with radii r and t.
12. Construct a third circle with radius s that is externally tangent to both the circles you constructed in exercise 11.