the sides of a triangle measure 4cm, 3 4cm, and 2 2 cm three circles are drawn with centres A,B,C - Maths - Circles

Question

the sides of a triangle measure 4cm, 3 4cm, and 2 2 cm three
circles are drawn with centres A,B,C in such a way that each circle
touches the other two what are the diameters of these circles

Ayush Jha · Accepted Answer

We have

Let the radius of the circles having centres A B and C be $r_{1}, r_{2}, r_{3}$ respectively Since AB = 4 cm BC = 3 4 cm and AC = 2 2 cm So, $r_{1} + r_{2} = 4 (1) r_{1} + r_{3} = 2 2 (2) r_{2} + r_{3} = 3 4 (3)$ Now (1)-(2) $r_{2} - r_{3} = 1 8$ (4) Now (3)+(4) $r_{2} = 2 6 c m S i m i l a r l y, r_{1} = 1 4 c m r_{3} = 0 8 c m$ Hence the diameters are 5 2 cm, 2 8 cm 1 6 cm

the sides of a triangle measure 4cm, 3.4cm, and 2.2 cm three circles are drawn with centres A,B,C in such a way that each circle touches the other two what are the diameters of these circles