Question

For part B I need help to solve and explain my reasoning with a two column proof.

Answer 1

Solution:

Given the circle;

From the circle above;

$\triangle COA\text{ and }\triangle COB\text{ are isosceles triangle}$

This is because;

$\begin{gathered} |OA|=|OC|=r \\ \\ and\text{ } \\ \\ |OC|=|OB|=r \end{gathered}$

Since two sides are equal, the triangles are isosceles triangles.

(b) The sum of angles in a triangle is 180 degrees.

Thus, the angle subtended at the circumference by a semi-circle is 90 degrees.

Hence, angle C is a right angle