# 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

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by sweetteacher

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by sweetteacher

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OA&OB are perpendicular [45degrees].

PM+MQ=PQ

PN+NR=PR

Take 2 tangents & add

PM=PQ+QN

PM=PN

Hence Proves

The Brainliest Answer!

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!

Hope it helps u!!!!!!!!!!

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