Question

Consider the circle below and all of its markings and then answer the following questions:

Answer 1

Answer:

$100^{\circ}$

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,$4\times 4.5=3\times x$

18=3x

$x=\frac{18}{3}=6$

Point P is the center of circle.

BD=BR+RD=3+6=9 units

Radius=$\frac{9}{2}=$4.5 units

a.Circumference of given circle =$2\pi r$

Circumference of given circle =$2\time \pi\times 4.5=9\pi$ units

Area of circle=$\pi r^2$

Area of circle=$\pi(4.5)^2=20.25 \pi$

Area of circle=$20.25\pi$ square units

b.We are given that

Arc COD measure=$100^{\circ}$

Arc BSA measure =$60^{\circ}$

We have to find the measure of angle CRB

Measure of angle CRD is the average of arc COD and BSA

Therefore,Angle CRD=$\frac{100+60}{2}=80^{\circ}$

$Angle CRB+angle CRD=180^{\circ}$ ( linear pair sum)

$angle CRB+80=180$

$angle CRB=180-80=100^{\circ}$

Hence, the measure of angle CRB=$100^{\circ}$

Answer 2

The usual definition of pi is the ratio of the circumference of a circle to its diameter, so that the circumference of a circle is pi times the diameter, or 2 pi times the radius.