Two circles having radii 3.5 cm and 4.8 cm touch each other internally. Find the distance between their centres.
Chapter 3 – CIrcle- Text Book Solution
Practice Set 3.2 | Q 1 | Page 58
Two circles having radii 3.5 cm and 4.8 cm touch each other internally. Find the distance between their centres.
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.
Explanation:-
We are given two circles with centres P and Q that touch each other internally at point R. Let QR = 3.5 cm and PR = 4.8 cm.
According to the theorem of touching circles, we have P-Q-R. Therefore, the distance between the centres of the circles is equal to the difference in their radii.
Hence, PQ = PR – QR = 4.8 cm – 3.5 cm = 1.3 cm.
Therefore, the distance between the centres of the circles is 1.3 cm.
Chapter 3 – Circle – Text Book Solution
Practice set 3.2 | Q 1 | Page 58
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