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प्रश्न
ABC is a triangle with AB = 10 cm, BC = 8 cm and AC = 6 cm (not drawn to scale). Three circles are drawn touching each other with the vertices as their centres. Find the radii of the three circles.
उत्तर
Let the radii of the circles with A, B and C as centres be r1, r2 and r3 respectively.
According to the given information,
AB = 10 cm = r1 + r2 … (1)
BC = 8 cm = r2 + r3 … (2)
CA = 6 cm = r1 + r3 … (3)
Adding equations (1), (2) and (3),
2(r1 + r2 + r3) = 24
r1 + r2 + r3 = 12 … (4)
Subtracting (1) from (4),
r3 = 12 – 10 = 2
Subtracting (2) from (4),
r1 = 12 – 8 = 4
Subtracting (3) from (4),
r2 = 12 – 6 = 6
Thus, the radii of the three circles are 2 cm, 4 cm and 6 cm.
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