Question

Circle O is shown on the coordinate plane below. PQ is a diameter of circle O.What is the circumference of circle O? If necessary, round your answer to the nearest tenth.

Answer 1

Circunference of a circle is found by 2π • radius

In the image we see a circle with center in x=-3. y= 2

Radius of circle can be found , with the segment OQ or segment OP. Because both are radius

Also radius can be found with segment QP and dividing by 2. (QP/2 ).

Use the first way, finding OQ.

Then have to use Pithagoras teorem that says

X^2 + Y^2 = R^2

where X= x-x'. Y= y-y'. R = radius

so then O, the center has coordinates (-3, 2 )

and Q has coordinates. ( 3,5 )

replace O by ( x,y). And replace Q by (x',y')

then (x - x')^2 + (y - y')^2 = R^2

(-3-3)^2 + ( 2 - 5)^2 = R^2

(-6)^2 + (-3)^2 = R^ 2

36 + 9 = 45 = R^2

Its found R^2, now rest to find R = √45 = 6.708

Now that is found R ,lets find 2•π•R

2•π•R = 42.15