A chord of length 8cm is drawn at a distance of 4cm from the centre of curvature of the circle . Find the radius of circle
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A chord of length 8cm is drawn at a distance of 4cm from the centre of curvature of the circle . Find the radius of circle
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Step-by-step explanation:
Let AB be the chord and O be the centre of the circle
Let OC be the perpendicular drawn from O to AB
We know, that the perpendicular to a chord, from the centre of a circle, bisects the chord.
∴AB=8 cm
AC2=CB2=2AB
AC2=CB2=28
AC2=CB2=4 cm
In △OCA,
OA2=OC2+AC2 (BY Pythagoras theorem)
⇒OA2=(3)2+(4)2=9+16=25
⇒OA=5 cm
Hence, radius of the circle is 5 cm.
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