Question

o is the centre of the circle,chords AB and CD intersect each other at P and PO bisects angle APD. IF AB=8CM ,OM Perpendicular AB and ON perpendicular CD find the length of ND​

Answer 1

Answer is 4 cm.

Step by step explanation :-

In ∆OPM and ∆OPN,

angle OPM = angle OPN { given }

angle OMP = angle ONP = 90°

OP = OP { common side }

therefore ,

∆OPM congruent to ∆ONP { ASA rule }

angle MOP = angle NOP { C.P.C.T. }

therefore AB = CD because equal chords subtends equal angle.

AB = CD { proved }

AB = CD = 8 cm

Now we know that perpendicular from the centre bisects chord.

ND = 1/2 × AB

$\color{Red}{ND\:=\:4\:cm}$

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