Angle Bisector and Triangle Side Lengths Comparison

Very Hard Geometry Lines And Angles

In triangle ABC, let angle A be an acute angle measuring $30^{ ext{o}}$. Point D lies on side BC such that segment AD is the bisector of angle A, dividing it into two equal angles.

Given that side AB has a length of 10 units and side AC has a length of 8 units, determine the relationship between the following quantities:

Quantity A: The length of segment AD (the angle bisector).

Quantity B: The length of segment BC.

Quantity A is greater than Quantity B.

Quantity A is less than Quantity B.

Quantity A is equal to Quantity B.

The relationship cannot be determined from the information given.

Hint

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