Question

2)
Thaee congruent circles with centers
P,Q,R having radius 10 CM touch at
Points L,M,N as shown in the figure
Find perimeter of ∆P,Q,R​

Answer 1

Answer:

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

(i) For the perimeter of ΔABC

⇒AB=(5+5) cm=10 cm

BC=(5+5) cm=10 cm

CA=(5+5) cm=10 cm

∴ Perimeter of ΔABC=AB+BC+CA=(10+10+10) cm=30 cm

(ii) Consider ΔADF

∵ From triangle ABC, all sides are equal.

∴∠A=60

o

[equilateral triangle]

AF=AD

∴∠F=∠D=x(let) [If 2 sides are equal then their opposite angles are also equal]

∴x+x+60=180

⇒2x=120

⇒x=60

o

∴ ADF is a equilateral triangle

∴DF=AD=5 cm.

Hence the length of DF is 5 cm

solution