Geometry

Properties of Circles

Circles - Central Angles

         

In the above diagram, if the radius of the circle is 1818 and the angle AOBAOB (central angle) is 30,{30}^\circ, what is the measure of the arc AB^?\widehat{AB} ?

In the above diagram, if angle CODCOD is θ2=123\theta_2={123}^\circ and the measures of arc AB^\widehat{AB} and arc CD^\widehat{CD} are 5 cm5\text{ cm} and 15 cm,15\text{ cm}, respectively, what is the angle θ1(=AOB)?\theta_1 (= \angle AOB)?

In the above diagram, AB\overline{AB} is a diameter of the circle centered at OO, ABDC\overline{AB} \parallel \overline{DC}, and BOC=θ=30.\angle BOC=\theta={30}^\circ. If the measure of the arc BC^\widehat{BC} is l1=12π cm,l_1=12\pi\text{ cm}, what is the measure of the arc CD^?\widehat{CD} ?

In the above diagram, AB\overline{AB} is a diameter of the circle centered at O,O, and OD=DE\lvert{\overline{OD}}\rvert=\lvert{\overline{DE}}\rvert and E=θ=15.\angle E=\theta={15}^\circ. If the measure of the arc BD^\widehat{BD} is 5 cm,5\text{ cm}, what is the measure of the arc AC^\widehat{AC} in cm?\text{cm} ?

Imagine a circle divided into equal sectors via nn straight lines that cross point OO, the center of the circle. Let sector ABOABO be one of those sectors. When n=20,n=20, what is OAB\angle OAB in degrees? (Round down to the nearest degree if there is a decimal.)

×

Problem Loading...

Note Loading...

Set Loading...