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

CBSE Class 10 Maths PYQ · Circles · Concentric Circles · 3 Marks · March 2023 · Standard

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763 Marks · March 2023 · Standard

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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Sol. AB is the chord of larger circle touching the smaller circle at P.
OA = $5$ cm, OP = $3$ cm
To find AB
OP $\perp$ AB (radius $\perp$ tangent)
AB is the chord of larger circle and OP $\perp$ AB
$\therefore AP = PB$
In right-angled $\Delta AOP$, $AP^2 = 5^2-3^2 = 16$
$AP = 4$ cm