F4 Circles (4): angles

O is the centre of the circle. Which of the following must be correct?

• $\angle OBC=\angle OCB$ .

• $\angle BAC=2\angle BOC$ .

• $\angle ABC=90\degree$ .

In the figure, AOB is a diameter.  x =

• $20\degree$ .

• $30\degree$ .

• $36\degree$ .

• $45\degree$ .

In the figure,  AOB is a diameter and CBD is a straight line.  x =

• $18\degree$ .

• $24\degree$ .

• $30\degree$ .

• $36\degree$ .

In the figure, O is the centre and AODC is a straight line.  x =

• $25\degree$ .

• $35\degree$ .

• $40\degree$ .

• $50\degree$ .

In the figure, AOB is a diameter and APC is a straight line. Which of the following must be true?

• AP = PC.

• OP // BC.

• OP = $\frac{1}{2}$  BC.

•  $\angle CAB=\angle CBA$  .

In the figure, which of the following must be diameter(s) of the circle?

• PR

• PQ

• QS