9.1. Parts of Circles & Tangent Lines http://www.ck12.org
52 + 552 =AC^2
25 + 3025 =AC^2
3050 =AC^2
AC=
√
3050 = 5
√
122
Tangent Segments
Let’s look at two tangent segments, drawn from the same external point. If we were to measure these two segments,
we would find that they are equal.
Theorem 10-2:If two tangent segments are drawn from the same external point, then the segments are equal.
The proof of Theorem 10-2 is in the review exercises.
Example 7:Find the perimeter of 4 ABC.
Solution:AE=AD,EB=BF, andCF=CD. Therefore, the perimeter of 4 ABC= 6 + 6 + 4 + 4 + 7 + 7 =34.
We say that
⊙
Gisinscribedin 4 ABC. A circle is inscribed in a polygon, if every side of the polygon is tangent to
the circle.
Example 8:IfDandAare the centers andAEis tangent to both circles, findDC.