EMAT 6700


Tangent Properties: Exercises

By Doug Westmoreland

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.


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