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Radii of two circles are 6.3 cm and 3.6 cm. State the distance between their centers if – i) they touch each other externally. ii) they touch each other internally.
Radii of two circles are 6.3 cm and 3.6 cm. State the distance between their centers if – i) they touch each other externally. ii) they touch each other internally.
Class 10 | Exercise 18A | ICSE | Maths | Selina | Tangents and Intersecting Chords
Radii of two circles are 6.3 cm and 3.6 cm. State the distance between their centers if – i) they touch each other externally. ii) they touch each other internally.

According to the given question

\[Radius\text{ }of\text{ }bigger\text{ }circle\text{ }=\text{ }6.3\text{ }cm\]and \[smaller\text{ }circle\text{ }radius\text{ }=\text{ }3.6\text{ }cm\]

i) The two circles touch each other at \[P\] point externally. \[O\text{ }and\text{ }O\]are the centers of the circles. Join \[OP\text{ }and\text{ }OP.\]

Selina Solutions Concise Class 10 Maths Chapter 18 ex. 18(A) - 12

So, \[OP\text{ }=\text{ }6.3\text{ }cm,\text{ }OP\text{ }=\text{ }3.6\text{ }cm\]

Thus, the distance between their \[centres\text{ }\left( OO \right)\]is given by

\[OO\text{ }=\text{ }OP\text{ }+\text{ }OP\]

\[=\text{ }6.3\text{ }+\text{ }3.6\text{ }=\text{ }9.9\text{ }cm\]

(ii)

Selina Solutions Concise Class 10 Maths Chapter 18 ex. 18(A) - 13

When the two circles touch each other at \[P\]internally. \[O\text{ }and\text{ }O\]are the centers of the circles. Join \[OP\text{ }and\text{ }OP\]

So, \[OP\text{ }=\text{ }6.3\text{ }cm,\text{ }OP\text{ }=\text{ }3.6\text{ }cm\]

Thus, the distance between their \[centres\text{ }\left( OO \right)\]is given by

\[OO\text{ }=\text{ }OP\text{ }\text{ }OP\]

\[=\text{ }6.3\text{ }-\text{ }3.6\text{ }=\text{ }2.7\text{ }cm\]

i

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