Home
Class 12
MATHS
Two circles with radii a and b touch eac...

Two circles with radii a and b touch each other externally such that `theta` is the angle between their direct common tangent(`a>b>=2`), then

Text Solution

Verified by Experts

As we can see that in the figure `C_1C_2BD` is a parallelogram
BD =a+b
AD= a-b
`sin( theta/2) = (AD)/(BD)`
`= (a-b)/(a+b)`
`theta/2 = sin^-1((a-b)/(a+b))`
`theta = 2sin^-1((a-b)/(a+b))`
Promotional Banner

Similar Questions

Explore conceptually related problems

Two circles with radii a and b touch each other externally such that theta is the angle between the direct common tangents,(a>b>=2). Then prove that theta=2sin^(-1)((a-b)/(a+b))

Two circles with radii a and b touch each other externally such that theta is the angle between the direct common tangents (agtbge2) , then

Two circles with radii a and b touch each other externally such that theta is the angle between the direct common tangents, (a > bgeq2) . Then prove that theta=2sin^(-1)((a-b)/(a+b)) .

Two circles with radii a and b touch each other externally such that theta is the angle between the direct common tangents, (a > bgeq2) . Then prove that theta=2sin^(-1)((a-b)/(a+b)) .

Two circles with radii a and b touch each other externally such that theta is the angle between the direct common tangents, (a > bgeq2) . Then prove that theta=2sin^(-1)((a-b)/(a+b)) .

Two circles with radii a and b touch each other externally such that theta is the angle between the direct common tangents, (a > bgeq2) . Then prove that theta=2sin^(-1)((a-b)/(a+b)) .

Two circles with radii aa n db touch each other externally such that theta is the angle between the direct common tangents, (a > bgeq2) . Then prove that theta=2sin^(-1)((a-b)/(a+b)) .

Two circles of radii a and b touch each other externally and theta be the angle between their direct common tangents (a>b>=2) then

Two circles with radii 3 cm and 2.5 cm touch each other externally then find the distance between their centre.

Two circles with radii 5 cm and 4.5 cm touch each other externally then find the distance between their centre.