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Standard X

Mathematics

Two Circles Touching Internally and Externally

If two circle...

Question

If two circles $C_{1}$ and $C_{2}$ have three points in common, then which one of the following is correct?

C_{1}

and

C_{2}

are cocentric

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C_{1}

and

C_{2}

are the same circle

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C_{1}

and

C_{2}

have different centres

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None of the above

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Solution

The correct option is B $C_{1}$ and $C_{2}$ are the same circle
We require 3 points to completely specific a circle & if 2 circles have same 3 points then they are same circle

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Similar questions

Q. If the two circles

C_{1}

and

C_{2}

have three points in common, then which of the following is correct?

C_{1}

and

C_{2}

are circles of unit radius with centres at

(0, 0)

and

(1, 0)

respectively.

C_{3}

is a circle of unit radius, passes through the centres of the circles

C_{1}

and

C_{2}

and have its centre above x-axis. Equation of the common tangent to

C_{1}

and

C_{3}

which does not pass through

C_{2}

$C_{1}, C_{2}$ are two circles of radii a, b (a < b) touching both the coordinate axes and have their centres in the first quadrant. Then the true statements among the following are

C_{1}

and

C_{2}

are two concentric circles, the radius of

C_{2}

being twice that of

C_{1}

. From a point

P

C_{2}

, tangents

P A

and

P B

are drawn to

C_{1}

. Prove that the centroid of the triangle

P A B

lies on

C_{1}

Q. The centres of two circles

C_{1}

and

C_{2}

each of unit radius are at a distance of 6 units from each other. Let

P

be the mid point of the line segment joining the centres of

C_{1}

and

C_{2}

and

C

be a circle touching circles

C_{1}

and

C_{2}

extemally. If a common tangent to

C_{1}

and

C

passing through

P

is also a common tangent to

C_{2}

and

C

, then the radius ofthe circle

C

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If two circles C1 and C2 have three points in common, then which one of the following is correct?

The correct option is B C1 and C2 are the same circleWe require 3 points to completely specific a circle & if 2 circles have same 3 points then they are same circle

If two circles $C_{1}$ and $C_{2}$ have three points in common, then which one of the following is correct?

The correct option is B $C_{1}$ and $C_{2}$ are the same circle
We require 3 points to completely specific a circle & if 2 circles have same 3 points then they are same circle