Answer
25
Explanation
AP is a tangent meeting a secant PB at P outside the circle.
(AP)² = (PE)(PB)
AP = 10 and BE = 21
So, let PE = y
10² = y(y+21)
10² = y² + 21y
y² + 21y = 100
y² + 21y + 10.5² = 100 + 10.5²
(y + 10.5)² = 210.25
(y + 10.5) = √210.25
= 14.5
y = 14.5 - 10.5 = 4 or y = -14.5 - 10.5 = -25
Since length cannot be negative, y = 4
BP = 21 + 4
= 25
