Three congruent circles with centres A,B and C with radius 5cm each, touch each other in point D,E,F as shown in figure. (i) What is the perimeter of ΔABC? (ii) What is the length of side DF of ΔDEF?
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Solution
Given A,B,C are congruent circles with radius =5cm each.
(i) For the perimeter of ΔABC
⇒AB=(5+5)cm=10cm
BC=(5+5)cm=10cm
CA=(5+5)cm=10cm
∴ Perimeter of ΔABC=AB+BC+CA=(10+10+10)cm=30cm
(ii) Consider ΔADF
∵ From triangle ABC, all sides are equal.
∴∠A=60o [equilateral triangle]
AF=AD
∴∠F=∠D=x(let) [If 2 sides are equal then their opposite angles are also equal]