Answer:
[tex]100^{\circ}[/tex]
Step-by-step explanation:
We are given that
AR=4
RC=4.5
BR=3
Let RD=x
Two chords are intersect to each other at R .
Product of AR and CR =product of BR and RD
Therefore,[tex]4\times 4.5=3\times x[/tex]
18=3x
[tex]x=\frac{18}{3}=6[/tex]
Point P is the center of circle.
BD=BR+RD=3+6=9 units
Radius=[tex]\frac{9}{2}=[/tex]4.5 units
a.Circumference of given circle =[tex]2\pi r[/tex]
Circumference of given circle =[tex]2\time \pi\times 4.5=9\pi[/tex] units
Area of circle=[tex]\pi r^2[/tex]
Area of circle=[tex]\pi(4.5)^2=20.25 \pi[/tex]
Area of circle=[tex]20.25\pi [/tex] square units
b.We are given that
Arc COD measure=[tex]100^{\circ}[/tex]
Arc BSA measure =[tex]60^{\circ}[/tex]
We have to find the measure of angle CRB
Measure of angle CRD is the average of arc COD and BSA
Therefore,Angle CRD=[tex]\frac{100+60}{2}=80^{\circ}[/tex]
[tex]Angle CRB+angle CRD=180^{\circ}[/tex] ( linear pair sum)
[tex]angle CRB+80=180[/tex]
[tex]angle CRB=180-80=100^{\circ}[/tex]
Hence, the measure of angle CRB=[tex]100^{\circ}[/tex]
