In this worksheet, we will practice using the angle bisector theorem, its converse, and the incenter theorem to solve various problems.

**Q2: **

In the figure, bisects , , , and the perimeter of is 57. Determine the lengths of and .

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

**Q3: **

Given that angle is bisected by , , , and . Determine the lengths and .

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

**Q4: **

If , , and , find the ratio between the areas of the and the .

- A
- B
- C
- D

**Q5: **

Find the lengths of and in the figure.

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

**Q6: **

If is a right-angled triangle at , , , and , calculate the value of .

**Q7: **

If is a quadrilateral in which , , , , where bisects and intersects at , find the value of the ratio .

- A
- B
- C
- D

**Q8: **

Given that is a triangle in which , find the value of each of and .

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

**Q9: **

In the triangle , , , and . Given that bisects and intersects at , determine the length of .

**Q10: **

Given that in the figure, , , and , what is ?

**Q11: **

If and , determine the perimeter of .

**Q12: **

Using the figure below, find the length of to the nearest hundredth.

**Q13: **

In triangle , lies on such that bisects . Given , , and , determine to the nearest hundredth.

**Q14: **

Use the figure to determine length to two decimal places.

**Q15: **

Given that , , and , what is ?

**Q16: **

is a right-angled triangle at , where bisects and intersects at . Given that , , determine the perimeter of .

**Q17: **

In the given figure, if , find .

- A
- B
- C
- D

**Q18: **

If and , find . Leave your answer as a fraction in its simplest form.

- A
- B
- C
- D

**Q19: **

Suppose that in the figure, . What is ?

**Q20: **

is a chord in a circle. major arc such that . is the midpoint of the minor arc . is drawn to intersect at . Determine the ratio between the areas of and .

- A1
- B2
- C4
- D

**Q21: **

is a triangle in which , , and . , where , and intersects at . If bisects , find the length of .

**Q22: **

Given that , , , and , find the numerical value of .

**Q23: **

In the shown figure, determine .

- A
- B
- C
- D

**Q24: **

is a triangle, where is the midpoint of , and . If the bisector of intersects at , find the value of .

- A
- B
- C
- D

**Q25: **

In the figure, . What is ?

- A
- B
- C
- D