Question

Circles with centre a b c touch each other externally if ab = 3 BC = 3 and ac = 4 then find the radii of circles

Answer 1

Step-by-step explanation:

Given Circles with centre a b c touch each other externally if ab = 3 BC = 3 and ac = 4 then find the radii of circles

• Let the radius of the circles centred at A, B and C be p,q,r respectively. As the circles touch each other externally and ab = 3 will be p + q = 3-------------1
• Also BC = 3 will be q + r = 3 ------------ 2
• Also ac = 4 will be p + r = 4---------------3
• Adding all the three equations we get
• 2(p + q + r) = 10
• Or p + q + r = 5 ---------------4
• Subtracting equation 2 from 4 we get
• So p + q + r – q – r = 54 – 3
• Or p = 2
• Now p + q = 3
• Or 2 + q = 3
• Or q = 1
• Now p + q + r = 5
• Or  2 + 1 + r = 5
• Or r = 5 – 3
• Or r = 2

Or the radii of the circles will be 2 cm, 1 cm and 2 cm

Reference link will be

https://brainly.in/question/7956450

Answer 2

Circle with centre a,b,c touch each other externally . If ab=3, bc=3, ac=4 then, the radii of circles will be2 cm, 1 cm and 2 cm.

Stepwise explanation is given below:

- In the given circles with centre a b c touch each other externally if ab = 3, bc = 3 and ac = 4 then find the radii of circles

- The radius of the circles centred at a,b and c be p,q,r respectively. As the circles touch each other externally and

ab = 3 will be p + q = 3......(1)

bc = 3 will be q + r = 3 ......(2)

ac = 4 will be p + r = 4......(3)

- Adding all the (1),(2) and (3) we get

2(p + q + r) = 10

p + q + r = 5 ......(4)

- Subtracting equation (2) from (4) we get

So, p + q + r – q – r = 54 – 3

p = 2

- Now p + q = 3

2 + q = 3

q = 1

- Now p + q + r = 5

2 + 1 + r = 5

r = 5 – 3

r = 2

- Or the radii of the circles will be 2 cm, 1 cm and 2 cm.