Question

In a circle with centre O segment OA perpendicular to chord PQ, l(PA) = 4cm, then l(AQ) = _______cm​

Answer 1

In given circle with centre O ,

Seg OA is Perpendicular to chord PQ

l ( PA ) = 4 cm

Therefore , l ( AQ) = ?

according to the theorem of circles ,

A perpendicular drawn from centre of circle to the chord bisects the chord.

Therefore , seg OA bisects the chord equally in two equal parts

i.e., l ( PQ ) = l ( PA) + l ( PQ)

l (PQ ) = 2 l ( PA )

PA = AQ

therefore , l ( AQ ) = 4 cm

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