Math, asked by VikkuShriyu, 9 months ago

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

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Answered by sonisiddharth751

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Answered by Anonymous

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

Given : Two circles of radii 3 cm & 5 cm with common centre.

[Refer the attachment for the diagram]

Let AB be a tangent to the inner/small circle and chord to the larger circle.

Let 'P' be the point of contact.

Construction : Join OP and OB.

Now, In ∆OPB ∠OPB = 90°

[radius is perpendicular to the tangent]

Using Pythagoras theorem

➳ 5² = 3² + PB²

➳ PB² = 25 - 9

➳ PB² = 16

➳ PB = √16

➳ PB = 4

⛬ PB = 4 cm

Now, AB = 2 × PB (The perpendicular drawn from the centre of the circle to a chord, bisects it)

➳ AB = 2 × 4 = 8 cm

⛬ The length of the chord of the larger circle which touches the smaller circle is 8 cm.

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