Secants and Tangents Section 10.4. By: Matt Lewis. Secants and Tangents. -Objectives Identify secant and tangent lines and segments. Distinguish between two types of tangent circles. Recognize common internal and common external tangents . Definitions.
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By: Matt Lewis
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Sample Problem #1
Step 1 - Constructing radius PB at the point of tangency as shown.
Since lengths of all the radii of a circle are equal, PB = 8.
Step 2 - Since the tangent and the radius at the point of tangency are always perpendicular, ΔABP is a right angled triangle.
Step 3 - Using the Pythagorean theorem,
Step 4 - Substituting for AP, AB and BP,
Step 5 - Since the negative value of the square root will yield a negative value for x, taking the positive square root of both sides,
x = 9.
Given: AC is Tangent to circle P
Calculate the value of X.
Sample Problem #2
OA is AP and OB PB.
AOBP is a quadrilateral.
90 + 90 + 140 + X = 360
X = 40
PA and PB are Tangents to Circle O.
a, b, and c.
JK is tangent to circles Q & P.
Given: Two tangent circles, is a common external tangent,
is the common internal tangent.
Prove: D is the midpt. of BC.
OS = 20
PS = 12
What is QS?
2. BC is a common
3. DA is a common
4. Any two tangents
drawn to a circle from
the same point are .
4. DB DA
5. DC DA
5. Same as 4.
6. DB DC
7. If a point divides
a line into two seg.,
then it is the midpt.
7. D is the midpt. of
Rhoad, Richard. Geometry for Enjoyment and Challenge. Boston: McDougal Littell, 1991.
Wolf, Ira. Barron’s SAT Subject Test- Math Level I. Barron Publishing, 2008.
27 May 2008.
Practice Problems Geometry.
http://www.hotmath.com, 27 May 2008.