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Two chords A B\ a n d\ C D of a circle ...

Two chords `A B\ a n d\ C D` of a circle are parallel and a line `l` is the perpendicular bisector of `A Bdot` Show that `l` bisects `C D`

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Two chords AB and CD of a circle are parallel and a line l is the perpendicular bisector of AB. Show that l bisects CD

Two chords AB and CD of a circle are parallel and a line l is the perpendicular bisector of AB. Show that l bisects CD

Knowledge Check

  • Two particles each of mass 'm' are placed at A and C are such AB=BC=L . The gravitational force on the third particle placed at D at a distance L on the perpendicular bisector of the line AC is

    A
    `(Gm^(2))/(L^(2))` along `BD`
    B
    `(Gm^(2))/(sqrt(2)L^(2))` along `DB`
    C
    `(Gm^(2))/(L^(2))` along `AC`
    D
    `(Gm^(2))/(sqrt(2)L^(2))` along `BD`

  • Observe the following facts for a parabola. (i) Axis of the parabola is the only line which can be the perpendicular bisector of the two chords of the parabola. (ii) If AB and CD are two parallel chords of the parabola and the normals at A and B intersect at P and the normals at C and D intersect at Q, then PQ is a normal to the parabola. For the parabola y^(2)=4x , AB and CD are any two parallel chords having slope 1. C_(1) is a circle passing through O, A and B and C_(2) is a circle passing through O, C and D. C_(1)andC_(2) intersect at

    A
    (4, -4)
    B
    (-4, 4)
    C
    (4, 4)
    D
    (-4, -4)

  • Observe the following facts for a parabola. (i) Axis of the parabola is the only line which can be the perpendicular bisector of the two chords of the parabola. (ii) If AB and CD are two parallel chords of the parabola and the normals at A and B intersect at P and the normals at C and D intersect at Q, then PQ is a normal to the parabola. The directrix of the parabola is

    A
    `y-1/24=0`
    B
    `y+1/24=0`
    C
    `y+1/12=0`
    D
    `y-1/12=0`

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    Theorem :-2The perpendicular from centre of a circle to the chord bisects the chord and Perpendicular bisectors of two chords of a circle intersects at the centre.

    In Figure, B M a n d D N are both perpendiculars to the segments A C a n d B M=D N . Prove that A C bisects B D

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