Question

(1) Three circles with centres A, B and C touch
each other pairwise externally. If AB =9 cm,
BC = 11 cm and AC = 10 cm, then find the
radii of the circles.
​

Answer 1

ANSWER:-

Given:

Three circles with centre A,B and C touch each other pairwise externally. If AB= 9cm, BC= 11cm and AC= 10cm.

To find:

Find the radii of the circle.

Solution:

⏺️AB= 9cm

⏺️BC= 11cm

⏺️AC= 10cm

Let, AR= AP= x cm

BQ= BP= y cm

CR= CQ= z cm

[since the length of tangents drawn from an external point arc equal]

Therefore,

AB= 9cm

=) AP + PB = 9cm

=) x + y= 9............(1)

Similarly,

=) y + z= 11..........(2)

&

=) z + x = 10.........(3)

Adding equation (1),(2)& (3), we get;

=) (x+y)+ (y+z)+ (z+x)= 30

=) 2(x+y+z)= 30

=) (x+y+z)= 15.........(4)

Now,

Subtracting, equation (4) -(2), we get;

x = 4

Hence,

The radii of the circle is 4cm.

Hope it helps ☺️