Question

OC is the bisector of angle AOB,P is any point on OC.From P,PM and PN are drawn perpendicular on OA and OB respectively. prove that MP= NP

Answer 1

OC is the bisector of angle AOB.

OA&OB are perpendicular [45degrees].

PM+MQ=PQ

PN+NR=PR

Take 2 tangents & add

PM=PQ+QN

PM=PN

Hence Proves

Answer 2

Given
OC bisects ∠AOB
PM and PN ⊥ OA andOB
To prove:MP=NP
proof:
In ΔMOP and ΔNOP
∠OMP=∠ONP=90°
∠MOP=∠NOP          (∵OA bisects ∠AOB)
OP=OP                    (common)
∴ΔMOP≈ΔNOP        (AAS congruence rule)
so,
MP=NP                    (By CPCT)
Hence proved!
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