12. Circles

12.01 Review: Circumference and area

12.02 Arc length and sector area

12.03 Extension: Chords of a circle

12.04 Inscribed angles and polygons

12.05 Angles from intersecting chords, secants, and tangents

Investigation: Construct a tangent to a circle from a point

12.06 Tangents to a circle

12.07 Lengths in chords, secants, and tangents

Investigation: Derive the equation of a circle from the Pythagorean theorem

12.08 Equations of circles

12.09 Review: Completing the square

12.10 Manipulating circle equations

United States of America UT

Math II

12.01 Review: Circumference and area

Interactive practice questions

Find the circumference of the circle shown, correct to two decimal places.

A circle is shown with a radius, indicated by a ray from the center to the circumference, labeled as $7$ cm. An arrowhead points from the circle's center along the radius to the edge, highlighting the direction of the measurement.

Easy

1min

Find the circumference of the circle shown, correct to one decimal place.

Easy

1min

Find the circumference of the circle shown, correct to two decimal places.

Easy

1min

Find the circumference of the circle shown, correct to three decimal places.

Easy

1min

Outcomes

II.G.GMD.1

Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. Use dissection arguments, cavalieri's principle, and informal limit arguments.

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