10.1 Tangent Properties to a Circle. POD 1. What measure is needed to find the circumference or area of a circle? 2. Find the radius of a circle with.

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Presentation transcript:

10.1 Tangent Properties to a Circle

POD 1. What measure is needed to find the circumference or area of a circle? 2. Find the radius of a circle with diameter 8 centimeters. 3. A right triangle has legs with lengths 5 inches and 12 inches. Find the length of the hypotenuse. 4. Solve 6x + 15 = 33

Vocab and theorems Circle – set of all points in a plane that are equidistant from a given point called the center. Radius – a segment whose endpoints are the center and any point on the circle. Chord – a segment whose endpoints are on a circle. Diameter – a chord that contains the center of the circle. Secant – a line that intersects a circle in two points. Tangent – a line in the plane of a circle that intersects the circle in EXACTLY one point, the point of tangency.

Theorems Theorem 10.1 – In a plane, a line is tangent to a circle if and only if the line is perpendicular to the radius of the circle at its endpoints on the circle. Theorem 10.2 – Tangent segments from a common external point are congruent.

Identify…

Lengths in a circle Use the diagram to find the given lengths Diameter of  P Diameter of  Q Radius of  P Radius of  Q

Circles… Circles can intersect at one, two or no points. Tangent Circles – Coplanar circles that intersect in one point Concentric Circles – Coplanar circles that have a common center.

Tangent Common Tangent – a line, ray or segment that is tangent to two coplanar circles

How many common tangents?

Prove it. Verify a tangent to a circle If AB is a radius of  A, show BC is tangent to  A.

Find the radius ST is tangent to Circle Q.Find the value of r.

Find the value of x