Question

Please help with geometry homework !

Answer 1

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