12.1 Parts of Circles and Tangent Lines Geometry

Parts of a Circle: Circle: The set of all points that are the same distance away from a specific point, called the center.Circle: The set of all points that are the same distance away from a specific point, called the center. The center of the circle is point A. We call this circle, “circle A,” and it is labeled The center of the circle is point A. We call this circle, “circle A,” and it is labeled Radii (the plural of radius) are line segments. There are infinitely many radii in any circle and they are all equal. Radii (the plural of radius) are line segments. There are infinitely many radii in any circle and they are all equal.

Parts of a Circle Defining Terms: Radius: The distance from the center to the circle. Radius: The distance from the center to the circle. Chord: A line segment whose endpoints are on a circle. Chord: A line segment whose endpoints are on a circle. Diameter: A chord that passes through the center of the circle. The length of the diameter is two times the length of a radius. Diameter: A chord that passes through the center of the circle. The length of the diameter is two times the length of a radius. Secant: A line that intersects a circle in two points. Secant: A line that intersects a circle in two points.

Parts of a Circle Defining Terms: The tangent ray TP and tangent segment are TP also called tangents. The tangent ray TP and tangent segment are TP also called tangents. Tangent: A line that intersects a circle in exactly one point. Tangent: A line that intersects a circle in exactly one point. Point of Tangency: The point where the tangent line touches the circle. Point of Tangency: The point where the tangent line touches the circle.

Find the parts of circle A that best fits the description. a) A radius b) A chord c) A tangent line d) A point of tangency e) A diameter f) A secant

Find the parts of circle A that best fits the description. Solutions: a) HA or AF b) CD; HF, or DG c) BJ d) Point H e) HF f) BD

Coplanar circles

Tangent Circles: When two circles intersect at one point. Concentric Circles: When two circles have the same center, but different radii. Congruent Circles: Two circles with the same radius, but different centers.

Determine if any of the following circles are congruent.

Internally & Externally Tangent Internally Tangent Circles: When two circles are tangent and one is inside the other. Externally Tangent Circles: When two circles are tangent and next to each other.

If circles are not tangent, they can still share a tangent line, called a common tangent. Common Internal Tangent: A line that is tangent to two circles and passes between the circles. Common External Tangent: A line that is tangent to two circles and stays on the top or bottom of both circles.

Tangent to a Circle Theorem A line is tangent to a circle if and only if the line is perpendicular to the radius drawn to the point of tangency.

Determine if the triangle below is a right triangle. Use the Pythagorean Theorem Use the Pythagorean Theorem 10 ² + 8² ?? (4  10)²   160 Therefore CB is not tangent to סּA.

Find AB in סּA and סּB. Simplify the radical. Use the Pythagorean Theorem Use the Pythagorean Theorem 5 ² + 55² = (AB)² = 3050 =  3050 = 5  122

Tangent Segments If two tangent segments are drawn from the same external point, then they are equal. BC  DC

Tangent Segments Find the perimeter of ∆ ABC. AE  AD thus AD = 6 BE  BF thus BF = 4 CF  CD thus CD = = 34

Tangent Segments If D and C are the centers and AE is tangent to both circles, find DC. Find DB using Pythagorean Th. 10 ² + 24² = (DB) ² = 676  676 = is to 5 what 26 is to BC BC = 13 BC + DB = DC = 39

Algebra Connection Find x 4x – 9 = 15 4x = x = 24 x = 6

Assignment: 12.1 from flexbook 1–9 13–17 19, 20 21–31 odd 32