MathematicsState true or false.If two equal chords AB and CD of a circle when produced intersect at a point P. Then PB = PD.

State true or false.


If two equal chords AB and CD of a circle when produced intersect at a point P. Then PB = PD.


  1. A
    True
  2. B
    False 

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    Solution:

    Given that, two equal chords AB and CD of a circle intersect at a point P when produced.
    Creating figures using given data. Now Joining OP and drawing OL ⊥  AB and OM ⊥  CD.
    In ΔOLP and ΔOMP  ,
    OL=OM                        (Equal chords are equidistant from the center)
    ∠  OLP =∠  OMP = 90 °   (From figure)
     OP=OP                        (Common side)
    By RHS congruence rule, Δ  OLP ≅Δ  OMP .
    And by C.P.CT. we have,
    LP=MP And AB=CD.
    Divide above relation by 2 from both sides,
    Since, the perpendicular distance from center to the circle bisects the chord, BL= 1 2 AB   And DM= 1 2 CD   .
    Now using equation 2 we have,
    BL=DM  Subtracting equation (3) from equation (1). Then we get,
    LP-BL=MP-DM
    ⇒  PB=PD
    Thus, option 1 is correct.
     
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