Question

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

a. What is the area and circumference of circle ? Explain how you calculated this answer.
b. If the arc measure of arc COD is 100 degrees and the arc measure of arc BSA is 60 degrees, what is the angle measure of angle CRB? Explain how you calculated this answer.

Answer 1

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.

Answer 2

`100^(\circ)`

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* 4.5=3* x`

18=3x

`x=(18)/(3)=6`

Point P is the center of circle.

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

Radius=
`(9)/(2)=`4.5 units

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

Circumference of given circle =
`2\time \pi* 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=
`(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)`