CK-12 Geometry-Concepts

http://www.ck12.org Chapter 9. Circles

9.

10.AandBare points of tangency for

⊙

Cand

⊙

D, respectively.

a. Is 4 AEC∼4BED? Why?

b. FindBC.

c. FindAD.

d. Using the trigonometric ratios, findm^6 C. Round to the nearest tenth of a degree.

11. Fill in the blanks in the proof of the Two Tangents Theorem.Given:ABandCBwith points of tangency atA
    andC.ADandDCare radii.Prove:AB∼=CB

TABLE9.1:

Statement Reason

1.

2.AD∼=DC

3.DA⊥ABandDC⊥CB

4. Definition of perpendicular lines


5. Connecting two existing points


6. 4 ADBand 4 DCBare right triangles
   7.DB∼=DB


7. 4 ABD∼= 4 CBD
   9.AB∼=CB
   12. From the above proof, we can also conclude (fill in the blanks):
   a.ABCDis a __ (type of quadrilateral).
   b. The line that connects the and the external pointB_____^6 ADCand^6 ABC.
   13. PointsA,B,C, andDare all points of tangency for the three tangent circles.ExplainwhyAT∼=BT∼=CT∼=DT.