Question

I need help to solve part B and give my reasoning in two collum proof.

Answer 1

3(a)

The diagram below would be helpful

From the diagram above, a segment has been made from C to O indicating the radius of the circle, so CO is a radius.

Also any line drawn from the center of a circle to touch the circumference is a radius, So, OB is a radius too.

Since CO and OB are radii of the circle, then their sides are equal,

Hence triangle COB is an isosceles triangle.

Also the line OA represents the radius of the circle just like CO. Since OA and CO are radii,

Hence triangle COA is an isosceles triangle.

(b) Statement: AOB is a straight line and at the center of a circle

Reason: Given

Statement: AOB is also an angle, which is 180 degrees

Reason: Angle on a straight line is 180 degrees

Statement: Angle AOB is an angle at the center of the circle, and angle C is at the circumference

Reason: same arc AB

Statement: Angle AOB = 2C

Reason: Angle at the center of a circle is twice angle at the circumference.

Hence

`\begin{gathered} \angle AOB=2\angle C \\ 180\degree=2C \\ C=(180)/(90) \\ C=90\degree \end{gathered}`

Therefore C is a right-angle (90 degrees)