Comparison of Triangle Altitude and Semi-Perimeter

Very Hard Geometry Triangles

Consider triangle ABC, where angle A measures $50^{ ext{o}}$ and angle B measures $70^{ ext{o}}$. Let point D be a point on line segment AC such that the length of segment AD is half the length of segment DC. Point E is the foot of the altitude from point B to line AC. Calculate the following quantities:

Quantity A: The length of segment BE.

Quantity B: The semi-perimeter of triangle ABC.

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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