Answer
△PCA and △PCB are congruent because of ASA. PA = PB since corresponding parts of a congruent triangle are congruent.
Work Step by Step
Proof:
ℓ is perpendicular to AB - given
ℓ bisects AB at C - given
AC ≅ CB - definition of bisect, both lengths are equal
∠ACP ≅ ∠BCP - definition of perpendicular, both angles are 90 degrees
PC ≅ PC - Reflexive Property of Congruence
△PCA ≅ △PCB - Postulate 4-3 Angle-Side-Angle (ASA) Postulate
PA = PB - Corresponding parts of ≅ △ are ≅