Question

Need help with two questions I am not good with this

Answer 1

Part 12)
`Center\ (2,-3),r=2\ units, (x-2)^2+(y+3)^2=4`

Part 13)
`m\angle ABC=47^o`

Explanation:

Part 12) we know that

The equation of a circle in center-radius form is equal to

`(x-h)^2+(y-k)^2=r^2`

where

(h,k) is the center of the circle

r is the radius of the circle

In this problem

Looking at the graph

The center is the
`point\ (2,-3)`

The radius is
`r=2\ units`

substitute in the expression above

`(x-2)^2+(y+3)^2=2^2`

`(x-2)^2+(y+3)^2=4`

Part 13) we know that

The measure of the external angle is the semi-difference of the arcs it covers.

so

`m\angle ABC=(1)/(2)[arc\ DE-arc\ AC]`

we have

`arc\ DE=142^o`

`arc\ AC=48^o`

`m\angle ABC=(1)/(2)[142^o-48^o]`

`m\angle ABC=47^o`