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…”