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Design an Ultimate Circle!$\newline$Name:$\newline$$\qquad$ Answer Key$\newline$Given information: $M R V=74 \quad m W P=3 \quad Q$ is tangent to $X$ at $U$$\newline$$x$ is the center $m z S=5 \quad m P O=9$$\newline$$2 y$ is the diameter $M S U=8 \quad M Q R=4$$\newline$m $260=60 \mathrm{~m} U Y=46 \mathrm{m \omega S}=16 \mathrm{~m} \angle \mathrm{WPO}=50$$\newline$($1$) Inscribed Angle/Arc:$\newline$$$m \angle Z U \omega=66 / 2=33^{\circ}$$$\newline$($4$) Central Angle / Arc:$\newline$$m \angle z \times W=66^{\circ}$$\newline$$$\begin{array}{l} \text { (3) Tangent / Chord: } \\ m \angle W U N=180-66=114 \\ 114+46=160 \\ 160 / 2=80^{\circ} 1 \end{array}$$$\newline$($10$)$\newline$Angles inside circle:$\newline$$$\begin{array}{l} m \angle U V Y=\frac{66+46}{2} \\ 112 / 2=156^{\circ} \mid \end{array}$$$\newline$Angles outside circle$\newline$$$m \angle R Q U=180-66=114$$$\newline$$$114+46=160 \quad \frac{160-74}{2}=\left|43^{\circ}\right|$$$\newline$Seyment of chords:$\newline$$$\begin{array}{l} m \overline{R S}=10 x=5(8) \\ 10 x=40 \quad x=14 \end{array}$$$\newline$($2$) Segment of secants:$\newline$$$\begin{aligned} \text { mYO }=51 & =16+4 x \\ 35 & =4 y \\ x & =18.751 \end{aligned}$$$\newline$($5$)$\newline$segment of secants and tangents:$\newline$$$m \overline{Q U}=$$$\newline$($2$)$\newline$Triangle sum theor $M R V=74 \quad m W P=3 \quad Q$$0$$\newline$Answers:$\newline$O Anna Taylor$\newline$http://www.teacherspayteachers.com/store/piece-of.-Pi