Question

In circle with centre O, chord AB and chord CD are at a distance 4 cm from the centre, then ​

Answer 1

Since chords equidistant from the centre of the circle are equal. ∴ AB = CD

Answer 2

Answer

Given:AB and CD are chords of a circle and they are equidistant 4cm from the center O.

OP and OQ are perpendiculars=4cm from O to AB and CD respectively.

∴ they bisect AB and CD

⇒AP=

2

1

AB and DQ=

2

1

DC

⇒∠OPA=∠OQD=90

∘

Now, between the △AOP and △DOQ we have

OP=OQ=4cm (given)

∠OPA=∠OQD=90

∘

⇒OB=OD (radii of the same circle)

∴△BOP is identical to △DOQ by RHS test

∴AP=DQ⇒AB=DC

⇒AB−DC=0

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