Home
Class 9
MATHS
The perpendicular from the centre of a c...

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

Text Solution

Verified by Experts

A perpendicular is drawn from the centre of a circle to the chord
To Find :
To prove that a perpendicular from the centre of a circle to a chord bisects the chord.
Solution :In triangle `OAC` and `OBC`,
`angleOCA = angleOCB` (both angles are` 90^@`)
`OA = OB ` (Radius of the circle)
`OC = OC` (common)
`triangleOAC cong triangleOBC`
`AC = BC` (Congruent parts of congruent triangles are equal)
Thus, C is the midpoint of the chord.
Therefore, the perpendicular drawn from the centre of a circle to a chord bisects the chord.
Hence proved.
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • AREA OF PARALLELOGRAMS AND TRIANGLES

    RD SHARMA|Exercise All Questions|205 Videos

  • CONGRUENT TRIANGLE

    RD SHARMA|Exercise All Questions|291 Videos

Similar Questions

Explore conceptually related problems

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.

What is the length of the perpendicular drawn from the centre of circle of radius r on the chord of length sqrt3

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

  • The straight line drawn from the centre of a circle perpendicular to a chord ul("P") the chord. A straight line will not cut a circle in more than ul("O") distinct points. ul("R") chords of a circle are equidistant from the centre of the circle.

    A
    `{:("P","Q","R"),("Trisect","Three","Perpendicular"):}`
    B
    `{:("P","Q","R"),("Defines","Two","Equal"):}`
    C
    `{:("P","Q","R"),("Bisects","Two","Equal"):}`
    D
    `{:("P","Q","R"),("Bisects","Three","Parallel"):}`

    • Similar Questions

    Explore conceptually related problems

    A line drawn drom the centre of a circle to a chord always bisects it. (True/False).

    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.

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

    PS is the chord of the circle with centre O . A perpendicular is drawn from centre O of the circle to chord PS at M. If overline(PS)=30 cm and overline(OM) =8 cm , then find the radius of the circle .

    PS is the chord of the circle with centre O. A perpendicular is drawn from centre O of the circle to chord PS at M. If bar(PS) =30 cm and bar(OM) =8 cm , then find the radius of the circle.

    Home
    Profile