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Question 7
Two concentric circles are of radii 5 cm and 3 cm. Find the length of the chord of the larger circle which touches the smaller circle.

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Solution


Let the two concentric circles with centre O.

AB be the chord of the larger circle which touches the smaller circle at point P.
AB is tangent to the smaller circle to the point P.
OPAB
By Pythagoras theorem in Δ OPA,
OA2=AP2+OP2
52=AP2+32
AP2=259
AP=4
In Δ OPB,
Since OP AB,
AP = PB ( Perpendicular from the centre of the circle bisects the chord)
AB = 2AP = 2 × 4 = 8 cm
The length of the chord of the larger circle is 8 cm.


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