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Geo.7 Circles

I know what chords, arcs, and central angles are.

I can use the relationship between central and inscribed angles to calculate angle measures and prove geometric theorems.
I know that an inscribed angle is half the measure of the central angle that defines the same arc.

I can use the relationship between tangent lines and radii to calculate angle measures and prove geometric theorems.
I know that a line tangent to a circle is perpendicular to the radius drawn to the point of tangency.

I can prove a theorem about opposite angles in quadrilaterals inscribed in circles.

I can construct the circumscribed circle of a triangle.
I can explain why the perpendicular bisectors of a triangle’s sides meet at a single point.

I can explain why the angle bisectors of a triangle meet at a single point.
I know any point on an angle bisector is equidistant from the rays that form the angle.

I can construct the inscribed circle of a triangle.

I can calculate lengths of arcs and areas of sectors in circles.

I can gather information about a sector to draw conclusions about the entire circle.

I know that when a circle is dilated, some ratios, like the ratio of the circumference to the diameter, stay constant.

I know that the radian measure of an angle whose vertex is the center of a circle is the ratio of the length of the arc defined by the angle to the circle’s radius.

I understand the relative sizes of angles measured in radians.

I can calculate the area of a sector whose central angle measure is given in radians.
I know that the radian measure of an angle can be thought of as the slope of the line $\ell=\theta \boldcdot r$.

I can use properties of circles to solve geometric problems.