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Standard X

Mathematics

Chord Properties of Circles

Radii of two ...

Question

Radii of two concentric circles are 40 cm and 41 cm. AB is a chord of the bigger circle and tangent to the smaller circle. Find the length of AB

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Solution

The correct option is D $18$
$O C = 40 c m, O B = 41 c m$

$O C ⊥ A B$ since AB is tangent to the smaller circle .

$⟹ A C + B C$

In $△ O C B$

$O B^{2} = O C^{2} + B C^{2}$

$⟹ B C^{2} = 41^{2} - 40^{2} = 818 \times 1$

$⟹ B C = 9 c m$

$⟹ A B = 2 B C = 18 c m$

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Radii of two concentric circles are 40 cm and 41 cm. AB is a chord of the bigger circle and tangent to the smaller circle. Find the length of AB

The correct option is D 18OC=40cm,OB=41cm OC⊥AB since AB is tangent to the smaller circle . ⟹AC+BC In △OCB OB2=OC2+BC2 ⟹BC2=412–402=818×1 ⟹BC=9cm ⟹AB=2BC=18cm

The correct option is D $18$
$O C = 40 c m, O B = 41 c m$

$O C ⊥ A B$ since AB is tangent to the smaller circle .

$⟹ A C + B C$

In $△ O C B$

$O B^{2} = O C^{2} + B C^{2}$

$⟹ B C^{2} = 41^{2} - 40^{2} = 818 \times 1$

$⟹ B C = 9 c m$

$⟹ A B = 2 B C = 18 c m$