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Theorem 10.5 : There is one and only one...

Theorem 10.5 : There is one and only one circle passing through three given non-collinear points.

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In `/_\OPM` and `/_\OQM`
`OM=OM` (common)
`/_OMP=/_OMQ` (Perpendicular angles)
`PM=QM`
By SAS congruency, `/_\OPM` and `/_\OQM` are congruent.
`OP=OQ`
Similarly, we can prove that, ...
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Theorem:- 3 There is one and only one circle passing through three non collinear points and If two circles intersects in two points; then the line joining the centres is perpendicular bisector of common chords

Knowledge Check

  • How many circles can pass through three non-collinear points?

    A
    one
    B
    two
    C
    zero
    D
    infinitely many

  • How many circles can pass through three collinear points?

    A
    one
    B
    two
    C
    zero
    D
    infinitely many

  • What is the number of planes passing through three non-collinear points?

    A
    3
    B
    2
    C
    1
    D
    0

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    Statement 1: The differential equation of all circles in a plane must be of order 3. Statement 2: There is only one circle passing through three non-collinear points.

    How many lines can be drawn passing through three non-collinear points

    Only one line can pass through a given point.

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