Question

Q.8) Three congruent circles
with centres A,B and C with
radius 6cm each touch each
other externally in points D,E,F
as shown in fig. What is the
perimeter of AABC ?​

Answer 1

Answer:

Given A, B, C are congruent circles with radius =5cm each.

(i) Perimeter of triangle ABC

⇒AB=5+5=10

BC=5+5=10

CA=5+5=10

∴ Perimeter of triangle ABC=AB+BC+CA=10+10+10

=30

(ii) Consider triangle ADE

∵ From triangle ABC, all sides are equal.

∴∠A=60

o

[equilateral triangle]

AE=AD

∴∠E=∠D [If 2 sides are equal then their opposite angles are also equal]

∴x+x+60=180

2x=120

x=60

o

∴ADE is equilateral triangle

∴DE=5cm.