Download 10.1 Use Properties of Tangents

Geometry Chapter 10: Properties of Circles 10.1-­‐ Use Properties of Tangents SWBAT: identify parts of a circle; use properties of tangents in circles. Common Core: G-­‐C.2, G-­‐C.4. (+), G-­‐C.5 Parts of Circles Vocabulary: Term Definition Example or Visual The set of all points in a ______________________________ that Circle are equidistant from a given point called the ____________________________. Radius The ________________________ from the center of the circle to a point on the _____________________. A _______________________________ whose endpoints lie on the Chord circle. A chord that contains the _____________________ of the circle. Diameter The diameter is ____________________ the length of the radius. Geometry Chapter 10: Properties of Circles Secant A line that _________________________________________ a circle in ____________________ points. A line in the plane of a circle that intersects the circle in Tangent _____________________________ one _________________________. Point of Tangency The ____________________ where a tangent line ___________________________ the circle. v Two circles are ______________________________ if they have the same radius. Example: Tell whether the line, ray, or segment is best described as a radius, chord, diameter, secant, or tangent of ⊙C. a. 𝐴𝐵 b. 𝐷𝐸 c. 𝐷𝐶 d. 𝐷𝐸 e. 𝐹𝐺 f. 𝐶𝐺 g. 𝐸𝐺 h. 𝐸𝐶 Geometry Chapter 10: Properties of Circles Example: Use the diagram to find the given lengths. a. Radius of ⨀𝐴 b. Diameter of ⨀𝐴 c. Radius of ⨀𝐵 d. Diameter of ⨀𝐵 Ø Two circles can intersect in two points, one point, or no points. Ø Coplanar circles that have a common center are called _______________________________. Common Tangents: A common _________________________ tangent intersects the segment that joins the two centers of the circles. A common _________________________ tangent does not intersect the segment that joins the two centers of the circles. Geometry Chapter 10: Properties of Circles Example: Tell how many common tangents the circles have and draw them. “Do Now” Give an example of each part of a circle using the diagram below. a. Center: ________________ b. Radius: ________________ c. Chord: ________________ d. Diameter: ________________ e. Secant: ________________ f. Tangent: ________________ g. Point of Tangency: ________________ •
A tangent line intersects a circle at exactly ___________________ point, called the point of tangency. •
A line is tangent to a circle if and only if it’s ___________________________ to a _______________________ drawn to the point of tangency. Example: In the diagram, 𝑅𝑆 is a radius of ⨀𝑅. Is 𝑆𝑇 tangent to ⨀𝑅? Geometry Chapter 10: Properties of Circles Example: In the diagram, B is a point of tangency. Find the radius r of ⨀𝐶. More Tangent Line Properties If two segments from the same If a polygon is circumscribed around a external point are tangent to a circle, circle, then all the sides of the polygon then they are _________________________. are ___________________________. Example: Find each value or measure. Assume that segments that appear to be tangent are tangent. a. b. Example: Find the perimeter of ∆𝐷𝐸𝐹. Geometry Chapter 10: Properties of Circles Practice: 11. Determine if 𝑋𝑌 is tangent to circle Z. Directions: Assume that segments that appear to be tangent are tangent. 12. Find x. 13. Find x. Geometry Chapter 10: Properties of Circles 14. Find x. 15. Find SV. 16. If 𝑃𝑄 = 4𝑥 + 2, 𝑄𝑅 = 7𝑥 − 19, and 𝑄𝑈 = 34, find 𝑆𝑇. 17. Find the perimeter of ∆𝐽𝐾𝐿.