Ineed to find the circumference of this shape for #31

Step-by-step explanation:

Assumptions

This isn't drawn exactly to scale I don't think. I also think you are intended to believe that the inscribed figure is a rectangle, but that is a huge assumption.

If I'm right and that is a rectangle then the diagonal of the rectangle is also the  diameter of the circle.

A diameter is also the hypotenuse of the two triangles formed by cutting the rectangle in half.

So let's go on.

Step One

Find the diagonal / hypotenuse.

a = 8 in

b = 6 in

c = ?

c^2 = a^2 + b^2

c^2 = 8^2 + 6^2

c^2 = 64 + 36

sqrt(c^2) = sqrt(100)

c = 10

Step 2

Find the radius of the circle

2*r = d

d = 10

2*r = 10

r = 10/2

r = 5

Step two

Find the circumference.

Circumference = 2*pi * r

Circumference = 2* pi * 5

Circumference = 10*pi      <<<<        Answer

That is one possibility for an answer

The other is to use 3.14 for pi

Circumference = 2*5*3.14 = 31.4  <<<< Answer

answer: option a.

step-by-step explanation:

you know that the quadrilateral opqr ( a four sided figure) is inscribed in circle. this means that all its vertices are on the circle.

then, by definition, the opposite angles of the quadrilateral are supplementary, this means that the sum of their measures is 180 degrees.

you can observe in the figure that the angles ∠opq   and the angle ∠orq   are opposite, therefore:

then, can be used to d to calculate the measure of ∠opq

tangent

step-by-step explanation: