10.1 Tangents to Circles. Geometry Mrs. Spitz Spring 2005. Objectives/Assignment. Identify segments and lines related to circles. Use properties of a tangent to a circle. Assignment: Chapter 10 Definitions Chapter 10 Postulates/Theorems pp. 599-601 #5-48 all. Some definitions you need.
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The terms radius and diameter describe segments as well as measures.Some definitions you need
QP, QR, and QS are radii of Q. All radii of a circle are congruent.Some definitions you need
A diameter is a chord that passes through the center of the circle. PR is a diameter.Some definitions you need
A tangent is a line in the plane of a circle that intersects the circle in exactly one point. Linej is a tangent.Some definitions you need
Tell whether the line or segment is best described as a chord, a secant, a tangent, a diameter, or a radius of C.
c. EG – a tangent because it intersects the circle in one point.
2 points of intersection.
No points of intersection
The lines j and k intersect CD, so they are common internal tangents.Ex. 2: Identifying common tangents
The lines m and n do not intersect AB, so they are common external tangents.Ex. 2: Identifying common tangents
In a plane, the interior of a circle consists of the points that are inside the circle. The exterior of a circle consists of the points that are outside the circle.
If l is tangent to Q at point P, then l ⊥QP.Theorem 10.1
If l ⊥QP at P, then l is tangent to Q.Theorem 10.2
Because 112 _ 602 = 612, ∆DEF is a right triangle and DE is perpendicular to EF. So by Theorem 10.2; EF is tangent to D.Ex. 4: Verifying a Tangent to a Circle
First draw it. Tangent BC is perpendicular to radius AB at B, so ∆ABC is a right triangle; so you can use the Pythagorean theorem to solve.Ex. 5: Finding the radius of a circle
c2 = a2 + b2
(r + 8)2 = r2 + 162
r 2 + 16r + 64 = r2 + 256
Square of binomial
Subtract r2 from each side.
16r + 64 = 256
Subtract 64 from each side.
16r = 192
r = 12
The radius of the silo is 12 feet.
IF SR and ST are tangent to P, then SR ST.Theorem 10.3