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AB and CD are chords intersecting at point P. OP bisects angle APD. If AB=8cm ,OM perpendicular to AB and ON perpendicular to CD . Find ND



In triangle OMP and ONP
OMP = ∠ONP (90’)
∠OPM = ∠OPN (given)
OP=OP (common side) 
Therefore OMP = ONP (they are congruent ) ….by AAS rule .
Therefore AB = CD
because equal chords of a circle subtends equal angle at the center. Now,
CD = 8 cm
We know that ,
Perpendicular from the center bisects the chord .
Therefore ND = 4 cm

I hope it helps…………….. 
3 4 3
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