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Question
Two circles having radii 3.5 cm and 4.8 cm touch each other internally. Find the distance between their centres.
Solution 1
It is given that two circle having radii 3.5 cm and 4.8 cm touch each other internally.
We know, the distance between the centres of the circles touching internally is equal to the difference of their radii.
∴ Distance between the centres of the two circles = 4.8 cm − 3.5 cm = 1.3 cm
Thus, the distance between their centres is 1.3 cm.
Solution 2
Let the two circles having centres P and Q touch each other internally at point R.
Here, QR = 3.5 cm, PR = 4.8 cm
The two circles touch each other internally.
By theorem of touching circles,
P − Q − R
PQ = PR − QR ......[The distance between the centres of circles touching internally is equal to the difference in their radii]
= 4.8 – 3.5
= 1.3 cm
∴ The distance between the centres of the circles is 1.3 cm.
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