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

12.02 Arc length and sector area

Interactive practice questions

If the circumference of the circle is equal to $144$144 cm, find the length of the solid arc.

A circle is depicted with its arc and two radii outlined with a solid green line, thus forming a sector, while the rest of the circle is represented with a dashed green line. The two radii of the sector, formed a central angle labeled as $160$ degrees.

Easy

1min

The diagram shows a sector of a circle of radius $4$4 units, formed from an angle of size $180^\circ$180°.

Find the exact length of the arc. Do not round your answer.

Easy

2min

The diagram shows a sector of a circle of radius $4$4 units, formed from an angle of size $135^\circ$135°.

Find the length of the arc rounded to two decimal places.

Easy

2min

The diagram shows a sector of a circle of radius $6$6 units, formed from an angle of size $290^\circ$290°.

Find the exact length of the arc.

Easy

3min

Outcomes

II.G.C.5

Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector.

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