Two circles of radii 5 cm and 3 cm are concentric. Calculate the length of a chord of the outer circle which touches the inner. - Noon Academy

Two circles of radii 5 cm and 3 cm are concentric. Calculate the length of a chord of the outer circle which touches the inner.

Class 10 | Exercise 18A | ICSE | Maths | Selina | Tangents and Intersecting Chords

Two circles of radii 5 cm and 3 cm are concentric. Calculate the length of a chord of the outer circle which touches the inner.

Selina Solutions Concise Class 10 Maths Chapter 18 ex. 18(A) - 5

Solution:

Given,

$OS\text{ }=\text{ }5\text{ }cm\text{ }and\text{ }OT\text{ }=\text{ }3\text{ }cm$

In right triangle

$OST$

, we have

$S{{T}^{2}}~=\text{ }O{{S}^{2}}~\text{ }O{{T}^{2}}$

$=\text{ }25\text{ }-\text{ }9$

$=\text{ }16$

So,

$ST\text{ }=\text{ }4\text{ }cm$

As we know,

$OT$

is perpendicular to

$SP\text{ }and\text{ }OT$

bisects chord

$~SP$

Thus,

$SP\text{ }=\text{ }2\text{ }x\text{ }ST\text{ }=\text{ }8\text{ }cm$

i

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