The complete question asks "If mDB = 60° and PE = 3, then PB =?"
The correct answer is C) PB = 6.
Explanation:
See the attached picture for reference.
We know
∠DBP = 60°
PB ≡ PD because they are both radius of the circunference, which means that ΔPDB is an isosceles triangle of base DB.
As a consequence, ∠DBP ≡ ∠PDB = 60°.
But then ∠DPB = 180 - 60 - 60 = 60°.
An isosceles triangles with all the angles measuring 60° is an equilateral triangle.
In an equilateral triangle, the height (DE) cuts into to equl parts the side PB, which means that PE = (1/2) PB
We know PE = 3, therefore
PB = 2 × PE
= 2 × 3
= 6
Hence, PB = 6.
