9.2. Tangent Lines http://www.ck12.org
- BecauseAEis tangent to both circles, it is perpendicular to both radii and 4 ABCand 4 DBEare similar. To find
DB, use the Pythagorean Theorem.
102 + 242 =DB^2
100 + 576 = 676
DB=
√
676 = 26
To findBC, use similar triangles.
5
10
=
BC
26
−→BC= 13
DC=AB+BC= 26 + 13 = 39
Practice
Determine whether the given segment is tangent to
⊙
K.1.
2.
3.Algebra ConnectionFind the value of the indicated length(s) in
⊙
C.AandBare points of tangency. Simplify all
radicals.
4.
5.
6.
7.
8.
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.- 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- Definition of perpendicular lines
- Connecting two existing points
- 4 ADBand 4 DCBare right triangles