Objective: SWBAT recognize tangents and secants; solve problems using the right angle formed by a tangent and a
radius; solve problems using tangents drawn from the same point.
Standards: G.C.2
Unit 3 Lesson 6
Task 1: Chords, Secants, and Tangents
The circle above has the items below. What do you think the definition of each is?
a) A chord
b) A secant
c) A radius
d) A tangent
Task 2: Relationship of Tangent to Radius
Tangent Perpendicular Theorem: A tangent to a circle is perpendicular to the radius at the point
of tangency.
PT is tangent to the circle with center at point O. Find x.
Objective: SWBAT recognize tangents and secants; solve problems using the right angle formed by a tangent and a
radius; solve problems using tangents drawn from the same point.
Standards: G.C.2
Task 3: Length of Line Segments
(Think about the following hints when answering the questions below: What is the angle measure
created by a tangent and a radius? What right triangles are in the diagram? What theorem can you
use to find the lengths of the sides of a right triangle?)
PT is tangent to the circle with center at point O.
 Find the length of segment PT:

Find the length of segment ST:
Task 4: Tangent from an External Point
Tangents from an External Point Theorem: Tangent segments to a circle from the same external
pint are congruent. In the second diagram, a circle is inscribed in a triangle. Use the Tangents
from an External Point Theorem to find the value of x.
Objective: SWBAT recognize tangents and secants; solve problems using the right angle formed by a tangent and a
radius; solve problems using tangents drawn from the same point.
Standards: G.C.2
Task 5: Circumscribed Angles
A circumscribed angle is an angle formed by two tangents. In this sketch, ∠TPS is a circumscribed
angle. Circumscribed Angle Theorem: When a circumscribed angle of a circle shares a common
chord with the central angle, the two angles are supplementary.
In the fist diagram, ∠TPS is supplementary to ∠TOS because they share the chord.

Look at circle C in the second diagram. If m∠VCX = 55°, find m∠P.
Reflect on your work:
Write a reflection about the ideas discussed in class today. Use the sentence starter below if you
find it to be useful.
“One way a tangent and a secant are different is…”