Question

# If line segment AD is an angle bisector and AB=6, AC = 10, and BD = 3, what must DC equal?

- 8
- 9
- 10
- 5

Hint:

### the angle bisector theorem is concerned with the relative lengths of the two segments that a triangle's side is divided into by a line that bisects the opposite angle. It equates their relative lengths to the relative lengths of the other two sides of the triangle.

## The correct answer is: 8

### Angle bisector theorem

Hence, the correct option is A.

Here, the value of DC is 5.

### Related Questions to study

### Choose the correct statement for the angle bisector theorem to the following triangle.

The base is divided in the same ratio as the sides containing the angle.

### Choose the correct statement for the angle bisector theorem to the following triangle.

The base is divided in the same ratio as the sides containing the angle.

### Theorem used to find the value of AB in the following figure

Here, AB = 4√2.

### Theorem used to find the value of AB in the following figure

Here, AB = 4√2.

### To find the value of AB in the figure, which theorem is used?

If two or more parallel lines are cut by two transversals, then they divide the transversals proportionally.

### To find the value of AB in the figure, which theorem is used?

If two or more parallel lines are cut by two transversals, then they divide the transversals proportionally.

### Which of the statements is true in the case of the given triangle?

The base is divided in the same ratio as the sides containing the angle.

### Which of the statements is true in the case of the given triangle?

The base is divided in the same ratio as the sides containing the angle.

### To find the value of *p, *which statements can be used?

Her, the value of p is 43.5.

### To find the value of *p, *which statements can be used?

Her, the value of p is 43.5.

### In the figure, to find the value of *x* which theorem can be used?

Here, the value of x is 10.

### In the figure, to find the value of *x* which theorem can be used?

Here, the value of x is 10.

It is also called basic proportionality theorem.

It is also called basic proportionality theorem.

### Find the length of the segment AB

It is also called basic proportionality theorem or Thales' theorem.

### Find the length of the segment AB

It is also called basic proportionality theorem or Thales' theorem.

### In the given triangle then the line segment DE ll AC

It is also called midpoint theorem.

### In the given triangle then the line segment DE ll AC

It is also called midpoint theorem.