9. $m\widehat{can} = 226^{\circ}$. find $m\widehat{cn}$.
10. $df = 30$. find the circumference of $\odot e$.
11. $m\widehat{dow} = 294^{\circ}$. find $m\widehat{dw}$.
12. $no = 24$. find the circumference of $\odot n$.
13. $uq = 13$. find the circumference of $\odot u$.
14. $on = 43$. find $ot$.
15. $is = 17$. find the circumference of $\odot r$.
16. $tv = 32$. find $uv$.

Question

Accepted Answer

{ "quality": "clear", "question_count": 8, "skills_matched": [ "step_cot", "table_formatter", "explain_then_answer", "tutor" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Arc Measure", "Circle Circumference", "Circle Radius and Diameter" ], "current_concepts": [ "Arc Measure", "Circle Circumference", "Circle Radius and Diameter" ] } ## Find the measure of arc MCN The measure of a full circle is $360^\circ$. The major arc $\widehat{CAN}$ has a measure of $226^\circ$. The remaining arc $\widehat{MCN}$ completes the circle: $$ m\widehat{MCN} = 360^\circ - m\widehat{CAN} = 360^\circ - 226^\circ = 134^\circ $$ ## Find the circumference of circle E The diameter of circle $E$ is $DF = 30$. The formula for the circumference $C$ using diameter $d$ is: $$ C = \pi d = 30\pi \approx 94.25 $$ ## Find the measure of arc MDW The major arc $\widehat{DOW}$ has a measure of $294^\circ$. The remaining arc $\widehat{MDW}$ completes the circle: $$ m\widehat{MDW} = 360^\circ - m\widehat{DOW} = 360^\circ - 294^\circ = 66^\circ $$ ## Find the circumference of circle N The radius of circle $N$ is $NO = 24$. The formula for the circumference $C$ using radius $r$ is: $$ C = 2\pi r = 2\pi(24) = 48\pi \approx 150.80 $$ ## Find the circumference of circle U The radius of circle $U$ is $UQ = 13$. The formula for the circumference $C$ is: $$ C = 2\pi r = 2\pi(13) = 26\pi \approx 81.68 $$ ## Find the length of OT The segment $ON$ is a radius of circle $O$, so $ON = 43$. Since $OT$ is also a radius of the same circle $O$, its length must be equal to $ON$: $$ OT = ON = 43 $$ ## Find the circumference of circle R The diameter of circle $R$ is $IS = 17$. The formula for the circumference $C$ is: $$ C = \pi d = 17\pi \approx 53.41 $$ ## Find the length of UV The segment $TV$ is a diameter of circle $U$ with length $TV = 32$. The segment $UV$ is a radius of circle $U$. The radius is half of the diameter: $$ UV = \frac{TV}{2} = \frac{32}{2} = 16 $$ | No. | Problem | Answer | |---|---|---| | 9 | $m\widehat{CAN}=226^\circ$. Find $m\widehat{MCN}$. | $134^\circ$ | | 10 | $DF=30$. Find the circumference of $\odot E$. | $30\pi \approx 94.25$ | | 11 | $m\widehat{DOW}=294^\circ$. Find $m\widehat{MDW}$. | $66^\circ$ | | 12 | $NO=24$. Find the circumference of $\odot N$. | $48\pi \approx 150.80$ | | 13 | $UQ=13$. Find the circumference of $\odot U$. | $26\pi \approx 81.68$ | | 14 | $ON=43$. Find $OT$. | $43$ | | 15 | $IS=17$. Find the circumference of $\odot R$. | $17\pi \approx 53.41$ | | 16 | $TV=32$. Find $UV$. | $16$ | { "subject": "Mathematics", "question_type": "Multi-part", "knowledge_point": [ "Mathematics", "Geometry", "Circle Properties" ] }

No.	Problem	Answer
10	\(DF=30\). Find the circumference of \(\odot E\).	\(30\pi \approx 94.25\)
11	\(m\widehat{DOW}=294^\circ\). Find \(m\widehat{MDW}\).	\(66^\circ\)
12	\(NO=24\). Find the circumference of \(\odot N\).	\(48\pi \approx 150.80\)
13	\(UQ=13\). Find the circumference of \(\odot U\).	\(26\pi \approx 81.68\)
14	\(ON=43\). Find \(OT\).	\(43\)
15	\(IS=17\). Find the circumference of \(\odot R\).	\(17\pi \approx 53.41\)
16	\(TV=32\). Find \(UV\).	\(16\)

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Question

Explanation:

Find the measure of arc MCN

Find the circumference of circle E

Find the measure of arc MDW

Find the circumference of circle N

Find the circumference of circle U

Find the length of OT

Find the circumference of circle R

Find the length of UV

Answer: