Three circles of radii 1cm, 2cm and 3cm touch each other externally. The area of the triangle formed by joining the center of the circle is?
A) 6cm
B) 12cm
C) 18cm
D) 24cm
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Step-by-step explanation: in image
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The area of the triangle formed by joining the centers of the circles is 6 cm²
Step-by-step explanation:
The three circles touch each other externally and thus joining their radii consecutively taken as a pair, we can find the sides of a triangle (see the given figure).
Then
the side AB (a) is (1 + 2) cm = 3 cm
the side BC (b) is (2 + 3) cm = 5 cm
the side CA (c) is (3 + 1) cm = 4 cm
Thus semi-perimeter (s) of ΔABC is
= (3 + 5 + 4)/2 cm = 6 cm
Therefore the area of ΔABC is
= √{s (s - a) (s - b) (s - c)}
= √{6 (6 - 3) (6 - 4) (6 - 5)} cm²
= √(6 * 3 * 2 * 1) cm²
= 6 cm²
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