Question

two concentric circle are of radii 5 cm and 3 cm. find the length of the chord of larger circle which touches the smaller circle

Answer 1

$\bf\huge{\underline{\underline{Question}}}$

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

$\bf\huge{\underline{\underline{Solution}}}$

In the figure, O is the common centre, of the given concentric circles.

AB is a chord of the bigger circle such that it is a tangent to the smaller circle P.

Since, OP is the radius of the smaller circle.

∴ OP ⊥ AB => ∠APO = 90°

Also, radius perpendicular to a chord bisects the chord

∴ OP bisects AB

=> AP = $\dfrac{1}{2}$

Now, in right ∆APO,

⠀ OA² = AP² + OP²

=> 5² = AP² + 3² => AP² = 5² - 3²

=> AP² = 4² => AP = 4cm

=> $\dfrac{1}{2}$ AB = 4 => AB = 2 × 4 = 8cm

Hence, the required length of the chord AB is 8cm.