Question

circles with centre A,B,C touch each other externally if AB=3cm,BC=3cm,CA=4cm.then find the radii of each circle
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Answer 1

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Answer 2

Radius of circle A = p = 2 cm

Radius of circle B = q = 1 cm

Radius of circle C = r = 2 cm

Step-by-step explanation:

Give that

AB = 3 cm

BC = 3 cm

CA = 4 cm

Let radius of circle A = p

Radius of circle B = q

Radius of circle C = r

From the figure

p + q = 3 ------ (1)

q + r = 3 ------ (2)

r + p = 4 ------ (3)

Add equation 1 & 2

⇒ p + 2 q + r = 6 ------- (4)

Put the value of r + p = 4 in above equation we get

⇒ 4 + 2 q = 6

⇒ 2 q = 2

⇒ q = 1

Put this value of q in equation 1 , we get

⇒ r = 3 - 1

⇒ r = 2

From equation 3

⇒ p = 4 - r

⇒ p = 4 - 2

⇒ p = 2

Therefore Radius of circle A = p = 2 cm

Radius of circle B = q = 1 cm

Radius of circle C = r = 2 cm