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Two circles with equal are intersecting ...

Two circles with equal are intersecting at the points (0, 1) and (0,-1). The tangent at the point (0,1) to one of the circles passes through the centre of the order circle. Then the distance between the centres of these circles is.

A

`sqrt2`

B

2

C

1

D

`2sqrt2`

Text Solution

Verified by Experts

The correct Answer is:
B
`PC_1=PC_2` =r (say )
`rArr DeltaC_1PC_2` is isosceles
`rArr ` (PM) is perpendicular to `(C_1C_2)` and bisects `angleC_1PC_2`
Also `PC_1` is tangent `rArr PC_1` is perpendicular to `PC_2`
`rArr angleC_1PM=45^@=angleC_2PM`
`rArr PC_1=sqrt2=PC_2{ because cos45^@=1/r}`

`rArr (C_1C_2)=sqrt(2+2)=2`
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