In the adjoining figure, three circles with centers PQ and R are drawn, such that the circles with centers Q and R touch each other externally and they touch the circle with center P , internally. If PQ=10 cm,PR=8 cm and QR=12 cm, then the diameter of the largest circle is

A
10 cm
B
20 cm
C
30 cm
D
40 cm

Solution:

It is given that three circles with centers PQ and

R

are drawn, such that the circles with centers

Q

and

R

touch each other externally and they touch the circle with center

P

, internally.
If

P Q = 10 cm, P R = 8 cm

and

Q R = 12 cm

.
We have to find the diameter of the circle.
Find the diameter r and q are the radii of the smaller circles. And PL and PM are the radius of the biggest circle.

Now, we know that,

Q R = R A + A Q = 12...... i

And

P R = 8 c m

and

P Q = 10 cm

P L = P M = P Q + q = P R + r

Radius of the biggest circle,

⇒ 10 + q = 8 + r

⇒ r − q = 2

.....(ii)
Adding equation (i) and (ii),

2 r = 14

⇒ r = 7
And q = 5.

P L = 8 + 7 = 15

Radius = 15 and hence diameter = 30 cm.
Hence, the diameter of the largest circle is 30 cm.
Therefore, option 3 is correct.

In the adjoining figure, three circles with centers PQ and $R$ are drawn, such that the circles with centers $Q$ and $R$ touch each other externally and they touch the circle with center $P$ , internally. If $P Q = 10 cm, P R = 8 cm$ and $Q R = 12 cm,$ then the diameter of the largest circle is

Solution:

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