http://www.ck12.org Chapter 9. Circles
BecauseAB⊥ADandDC⊥CB,ABandCBare tangent to the circle and also congruent. SetAB=CBand solve for
x.
4 x− 9 = 15
4 x= 24
x= 6Watch this video for help with the Examples above.
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Click image to the left for more content.CK-12 Foundation: Chapter9TangentLinesB
Vocabulary
Acircleis the set of all points that are the same distance away from a specific point, called thecenter. Aradius
is the distance from the center to the outer rim of a circle. Adiameteris a chord that passes through the center of
the circle. The length of a diameter is two times the length of a radius. Atangentis a line that intersects a circle in
exactly one point. Thepoint of tangencyis the point where the tangent line touches the circle.
Guided Practice
- Determine if the triangle below is a right triangle. Explain why or why not.
- Find the distance between the centers of the two circles. Reduce all radicals.
- IfDandAare the centers andAEis tangent to both circles, findDC.
Answers:
- To determine if the triangle is a right triangle, use the Pythagorean Theorem. 4
√
10 is the longest length, so we
will set it equal tocin the formula.
82 + 102?
(
4
√
10
) 2
64 + 1006 = 160
4 ABCis not a right triangle. And, from the converse of the Tangent to a Circle Theorem,CBis not tangent to
⊙
A.- The distance between the two circles isAB. They are not tangent, however,AD⊥DCandDC⊥CB. Let’s addBE,
such thatEDCBis a rectangle. Then, use the Pythagorean Theorem to findAB.