Lesson 19.2 and 19.3

Lesson 19.2: Angles in Inscribed Quadrilaterals Theorem: If a quadrilateral is inscribed in a circle, then its opposite angles are supplementary. Converse: If a quadrilateral’s opposite angles are supplementary, then it can be inscribed inside a circle.

Lesson 19.3: Tangents and Circumscribed Angles A secant is a line that intersects a circle in two points. A tangent is a line in the plane of a circle that intersects the circle in exactly one point. The point where the tangent intersects the circle is called the point of tangency.

Identify all special points, segments and lines in the picture.

Tangent-Radius Theorem If a line is tangent to a circle, then it is perpendicular to a radius drawn to the point of tangency.

Circumscribed Angle Theorem A circumscribed angle to a circle and its related central angle are supplementary.

Example Find the measure of arc BD.

Theorem Tangent segments from a common external point are congruent.

Example Solve for x.