Mathematics
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.
Circles
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Answer
Let O be the center of the circle with radius = 6.3 cm and O' be the center of circle with radius = 3.6 cm.
(i) When the two circles touch each other at P externally. O' and O are the centers of the circles. Join O'P and OP.
So, O'P = 6.3 cm, OP = 3.6 cm
Hence, the distance between their centres (O'O) is given by
O'O = O'P + OP = 6.3 + 3.6 = 9.9 cm.
Hence, distance between their centers if they touch each other externally is 9.9 cm.
(ii) When the two circles touch each other at P internally, O and O' are the centers of the circles. Join OP and O'P.
So, O'P = 6.3 cm, OP = 3.6 cm.
Hence, the distance between their centres (O'O) is given by
O'O = O'P - OP = 6.3 - 3.6 = 2.7 cm.
Hence, distance between their centers if they touch each other internally is 2.7 cm.
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