Angles in Circles Review

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Presentation transcript:

Angles in Circles Review Central angles, inscribed, tangent chord, vertex interior, vertex exterior

Radius A radius is the distance from the center of the circle to a point on the circle

Diameter A diameter is the distance across the circle through its center. It is made up of two radii. Therefore, we have two equations for the relationship between a radius and diameter

Central Angles In a central angle, the vertex of the angle is on the CENTER of the circle. vertex

Central Angles The measure of the central angle is EQUAL to the measure of its intercepted arc.

Central Angles Find the measure of arc HJ & arc FGH

Central Angles Find the measure of arc CDE & arc BCD

Central Angles Find the measure of arc LMN & arc LNP

Inscribed Angles In an inscribed angle, the vertex of the angle is on the EDGE of the circle. vertex

Inscribed Angles The measure of the inscribed angle is HALF of the measure of its intercepted arc.

Inscribed Angles Solve for x and y.

Inscribed Triangles If an inscribed triangles hypotenuse is the diameter of the circle, it is a right triangle.

Inscribed Triangles Solve for x and y.

Inscribed Triangles Solve for x, y, and z.

Inscribed Quadrilaterals The OPPOSITE angles in an inscribed quadrilateral are SUPPLEMENTARY.

Inscribed Quadrilaterals Solve for x and y.

Inscribed Quadrilaterals Solve for x, y, and z.

Vertex : ON the circle vertex

Vertex : ON the circle The rule is the same as inscribed angles. The measure of the angle is HALF the measure of its intercepted arc.

Vertex : ON the circle Solve for x and y.

Vertex : ON the circle Solve for x and y.

Vertex : ON the circle

Vertex : INSIDE the circle

Vertex : INSIDE the circle

Vertex : INSIDE the circle

Vertex : INSIDE the circle

Vertex : INSIDE the circle

Vertex : OUTSIDE the circle

Vertex : OUTSIDE the circle

Vertex : OUTSIDE the circle

Vertex : OUTSIDE the circle

Vertex : OUTSIDE the circle

Vertex : OUTSIDE the circle