Question

in this ques o is the centre of the circle but I want to ask whether o is the midpoint of PQ chord?


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Answer 1

Step-by-step explanation:

Solution



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Given : In the figure , O is center of the circle of the chord , And AB  is chord . P is a point on AB such that AP=PB , We need to prove that , OP⊥AB 

Construction : Join OA and OB

 

In ΔOAP and ΔOBP 

OA=OB       [raddi of the same circle]

OP=OP               [common]

AP=PB          [Given]

By side- side - side criterion  of congruency , 

ΔOAP≅ΔOBP

The corresponding parts of the congruent triangle are congruent .

∴∠OPA=∠OPB    [by c.p.c.t]

But∠OPA+∠OPB=180o   [linear pair]

∴∠OPA=∠OPB=90o

HenceOP⊥AB 

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