lengths associated with circles lesson

 $\angle TRN$  is an inscribed angle, so it's half as big as arc TN.  What other angle in the diagram is half as big as arc TN?

•  $\angle RWN$  

•  $\angle PTR$  

•  $\angle PNR$  

•  $\angle TPN$  

•  $\angle TWP$  

Tags

CCSS.HSG.C.A.2

 $\angle PTR$  is an inscribed angle, so it's half as big as arc PR.  What other angle in the diagram is half as big as arc PR?

•  $\angle TPN$  

•  $\angle TRN$  

•  $\angle PNR$  

•  $\angle RWN$  

•  $\angle TWP$  

Tags

CCSS.HSG.C.A.2

 $\angle RWN$  is vertical to what other angle?

•  $\angle TPN$  

•  $\angle TRN$  

•  $\angle PNR$  

•  $\angle PTR$  

•  $\angle TWP$  

Tags

CCSS.7.G.B.5

Now that you know that all three pairs of angles are congruent, what triangle is similar to $\Delta PWT$ by AA~?

•  $\Delta RWN$  

•  $\Delta RNW$  

•  $\Delta NRW$  

•  $\Delta WRN$  

•  $\Delta WNR$  

Tags

CCSS.8.G.A.2

CCSS.HSG.CO.B.6

Now that you know that $\Delta PWT\ \sim\ \Delta RWN$  write the other half of the proportion  $\frac{PW}{WT}\ =\ ?$  

•  $\frac{WR}{RN}$  

•  $\frac{NW}{WR}$  

•  $\frac{WN}{NR}$  

•  $\frac{RN}{NW}$  

•  $\frac{RW}{WN}$  

Tags

CCSS.HSG.SRT.A.2

Now cross multiply $\frac{PW}{WT}\ =\ \frac{RW}{WN}$  to get an equation we'll call the power of a point for W.

•  $\left(PW\right)\left(WT\right)\ =\ \left(RW\right)\left(WN\right)$  

•  $\left(PW\right)\left(WN\right)\ =\ \left(WT\right)\left(RW\right)$  

•  $\left(PW\right)\left(RW\right)\ =\ \left(WT\right)\left(WN\right)$  

•  $\left(PW\right)\left(NW\right)\ =\ \left(RT\right)\left(WT\right)$  

Tags

CCSS.HSG.C.A.2

How long is the segment marked N in the diagram? Please enter JUST the number.

(a)  

Answer explanation

(5)(12) = (N)(10)

Tags

CCSS.HSG.C.A.2

 $\angle ESN$  is an inscribed angle, so it's half as big as arc EN.  What other angle in the diagram is half as big as arc EN?

•  $\angle ETN$  

•  $\angle EAN$  

•  $\angle SET$  

•  $\angle TCS$  

•  $\angle ANS$  

Tags

CCSS.HSG.C.A.2

 $\angle SAN$  is congruent to what other angle by the reflexive property?

•  $\angle EAT$  

•  $\angle NAT$  

•  $\angle SAE$  

•  $\angle CAE$  

Tags

CCSS.HSG.CO.C.9

Now that you know that two pairs of angles are congruent, what triangle is similar to $\Delta EAT$ by AA~?

•  $\Delta CNT$  

•  $\Delta NAS$  

•  $\Delta ANS$  

•  $\Delta ESC$  

Tags

CCSS.HSG.SRT.A.2