Question

2) In the figure, A and B are the centres of
two circles touching each other externally
at M. Line AC and line BD are the
tangents. If AD=6 cm, BC = 9 cm, then
find the lengths of seg AC and seg BD.
D C
M​

Answer 1

In the figure, A and B are the centres of

two circles touching each other externally

at M. Line AC and line BD are the

tangents. If AD=6 cm, BC = 9 cm, then

the lengths of seg AC = 12cm and seg BD = 13.75cm.

• Given that : AC is perpendicular to BC, AD is perpendicular to BD, AD=6 cm and BC = 9 cm.

• Here, AD and BC are the radii of the two circles, respectively.

• As the two circles are touching each other externally so,

AB = sum of the radii of both circles

• AB = 6+9 = 15cm

• Both the triangles ABD and BAC are right angled triangles.

• By applying Pythagoras theorem in both the triangles, we get the lengths of the segments AC and BD as 12cm and 13.75cm, respectively.