In this worksheet, we will practice using the properties of tangents to find the measure of an angle of tangency or an inscribed angle with it in the same arc.

**Q5: **

Given that , find .

**Q6: **

Given that is a tangent to the circle and , find and .

- A ,
- B ,
- C ,
- D ,

**Q7: **

Find .

**Q8: **

Given that is a tangent to the circle, and , determine and .

- A ,
- B ,
- C ,
- D ,
- E ,

**Q9: **

If and , find .

**Q10: **

Given that is a tangent to the circle, and , find and .

- A ,
- B ,
- C ,
- D ,

**Q11: **

Given that and , find and .

- A78, 84
- B54, 84
- C54, 126
- D48, 84
- E78, 102

**Q12: **

Given that , find and .

- A ,
- B ,
- C ,
- D ,
- E ,

**Q13: **

Given that , find .

- A
- B
- C
- D

**Q14: **

In the figure, is a diameter of circle . Given that , find .

**Q15: **

Find .

**Q16: **

Find .

**Q17: **

If , find .

**Q18: **

If and are tangents to the circle and , find .

**Q19: **

Find .

**Q20: **

Given the figure below, find and .

- A ,
- B ,
- C ,
- D ,

**Q21: **

Given that , where and are tangent to the circle at and , find .

**Q22: **

Given that , determine and .

- A ,
- B ,
- C ,
- D ,

**Q23: **

Given that , find .

**Q24: **

A circle with centre has diameter . If and are two tangents to the circle, what can you say about them?

- Athey are intersecting
- Bthey are perpendicular
- Cthey are parallel

**Q25: **

Triangle is right angled at . Given that , , and is the circle that lies on and and is tangent to at , determine the area of to the nearest tenth of a square centimeter.