F4 Circles (10): Angle in alternate segment

PQ is the tangent to the circle at T. Name an angle in alternate segment (by the three vertices, no need to insert angle sign) corresponding to the angle x.

PQ is the tangent to the circle at T. Name an angle in alternate segment (by the three vertices, no need to insert angle sign) corresponding to the angle x.

PQ is the tangent to the circle at T.  What is x ? (no need to input unit in your answer)

PQ is the tangent to the circle at T.  If $\angle BAT=28\degree$ , then y =  

•  $28\degree$  .

•  $32\degree$  .

•  $36\degree$  .

•  $38\degree$  .

PR and PQ are tangents to the circle at A and B respectively.  What is $\angle ABC$  ? (no need to input unit in your answer)

PR and PQ are tangents to the circle at A and B respectively.  It is known that  $\angle ABC=72\degree$ .  What is $\angle ARC$  ? (no need to input unit in your answer)

In the figure, CT is tangent to the circle at T and ABC is a straight line. Name ONE triangle similar to  $\Delta TBC$ 

 (Please follow the corresponding vertices).

In the figure, In the figure, CT is tangent to the circle at T and ABC is a straight line.  It is known that  $\Delta TBC$   is similar to  $\Delta ATC$  .   If  $TC=6$  and  $BC=4$  , then  $AB=$  

• 5

• 6

• 7.5

• 9