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Theorem 10.3 : The perpendicular from th...

Theorem 10.3 : The perpendicular from the centre of a circle to a chord bisects the chord.

Text Solution

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In `/_\OXA` and `/_\OXB`,
`/_OXA=/_OXB` (perpendicular angles)
`OA=OB` (Radius)
`OX-=OX` (Common)
By RHS rule, `/_\OXA` and `/_\OXB` are congruent.
`AX=BX` (CPCT)
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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.

Theorem 10.4 : The line drawn through the centre of a circle to bisect a chord is perpendicular to the chord.

Knowledge Check

  • The radius of a circle is 6 cm. The perpendicular distance from the centre of the circle to the chord which is 8 cm in length is

    A
    `sqrt(5)` cm
    B
    `2 sqrt(5)` cm
    C
    `2 sqrt(7)` cm
    D
    `sqrt(7)` cm

  • A 5 cm long perpendicular is drawn from the centre of a circle to a 24 cm long chord. Find the diameter of the circle.

    A
    A) 26 cm
    B
    B) 32 cm
    C
    C) 13 cm
    D
    D) 30 cm

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    The radius of a circle is 10 cm and the perpendicular form the centre to a chord is 8cm. Find the length of the chord. (ii) The radius of a circle is 10 cm. its one chord is 16 cm long. Find the perpendicular distance of this chord form the centre. (iii) in the adjoining figure O is the centre of circle. the radius of circle is 17 cm . if OC=8cm, then find the length of chord AB. (iv) In the adjoining figure, OMbotAB , radius OC=5cm and chord AB=8cm .Find the length of OM.

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