SECTION 10.5Tangents

TANGENTS

How can I use the properties of tangents to solve problems?

TANGENT

Tangent: A line that intersects the circle in exactly 1 point.

THEOREM

Theorem 10.9: If a line is tangent to a circle, then it is perpendicular to the radius drawn to the point of tangency.

THEOREM

Theorem 10.10: If a line is perpendicular to a radius of a circle, then the line is tangent to the circle.

THEOREM

Theorem 10.11: If two segments from the same exterior point are tangent to a circle, then they are congruent.

EXAMPLE

is tangent to Q at point R. Find y.

20

y

EXAMPLE

Determine whether is tangent to .

EXAMPLE

Determine whether is tangent to .

EXAMPLE

Determine whether is tangent to .

EXAMPLE

Find x. Assume that segments that appear tangent to circle are tangent.

EXAMPLE

Find a. Assume that segments that appear tangent to circle are tangent.

CIRCUMSCRIBED POLYGONS

Circumscribed Polygon: When a circle is inside a polygon and every side of the polygon is tangent to the circle.

Which one?

EXAMPLE

Triangle NOT is circumscribed about . Find the perimeter of if CT = NC – 28.

HOMEWORK

Page 556 #8 – 28 Even, skip 22 38, 40

LESSON PLAN

Intro Define a tangent and its relationship to a circle’s

radius Standards- 9.5 Supplies – slides, whiteboard, note sheets Timing: One day for notes, one day for a

combined review of 10.5 and 10.6 and a quiz. Day 1:

Essential Questions- slides 2 Input-slides 3 - 6, 13 Guided Practice - slides 7 – 12, 14, 15 Independent Practice – Book Work