Answer
4
Explanation
AP is a tangent meeting a secant BP at P outside the circle.
(PA)² = (PE)(PB)
PA = 6 and chord BE= 5.
Let PE = x
6² = x(x+5)
36 = x² + 5x
x² + 5x + 2.5² = 36 + 2.5²
(x + 2.5)² = 42.25
(x + 2.5) = √ 42.25 = 6.5
x = 6.5 - 2.5 = 4 or x = -6.5 - 2.5 = -9
But since length cannot be negative, x = 4.
