The lengths of parallel chords which are on same side of the centre of a circle are 6 cm and 8 cm. If radius of circle is 5 cm, then the distance between these chords is
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The lengths of parallel chords which are on same side of the centre of a circle are 6 cm and 8 cm. If radius of circle is 5 cm, then the distance between these chords is
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Answer:
5 cm
Step-by-step explanation:
Let AB and CD are two parallel chords of a circle having length 6 cm and 8 cm and radius is O.
Let the radius of the circle be r.
Now draw OP perpendicular to AB and OQ perpendicular to CD.
since OP is perpendicular to AB and OQ is perpendicular to CD and AB || CD
From figure, OP = 4 cm.
P, Q are the mid points of AB and CD respectively. [perpendicular from center bisects the chord]
So AP=PB=
2
AB
=
2
6
=3cm
CQ=QD=
2
CD
=
2
8
=4cm
Now in triangle OAP
OA
2
=OP
2
+AP
2
r
2
=16+9
r=
16+9
r=5cm