Home
Class 9
MATHS
Prove that the right bisector of a chor...

Prove that the right bisector of a chord of a circle, bisects the corresponding arc or the circle.

Text Solution

Verified by Experts

Let `AB` be a chord of a circle `C(O,r)`.
Let `PQ` be the right bisector of a chord `AB`, intersecting it at `L` and the circle at `P` and `Q`.
Since the right bisector of a chord always pass through the centre of the circle, `PQ` must pass through O
Join `OA ` and `OB`.
`OA` `=` `OB` [each equal to `r`]
`/_ALO = /_BLO `[ each eqal to `90^(@)` ]
`OL = OL ` [common]
`:. Delta OLA ~= Delta OLB `
`implies /_AOL= /_ BOP`
`implies m (hat(AP))=m( hat(BP))`
`implies hat(AP) ~= hat(BP)`.

Note the right bisector of a chord also bisects the corresponding major arc.
Promotional Banner

Similar Questions

Explore conceptually related problems

Prove that the perpendicular bisector of a chord of a circle always passes through the centre.

Prove that the diameter is the greatest chord in a circle.

If two arcs of a circle are congruent; then corresponding chords are equal

If two equal chords of a circle in intersect within the circle,prove that : the segments of the chord are equal to the corresponding segments of the other chord.the line joining the point of intersection to the centre makes equal angles with the chords.

If the length of an arc of a circle of radius a is equal to that of an arc of a circle of radius 2a, then the angle of the corresponding sector of the first circle is double the angle of the corresponding sector of the other circle. Is this statement false? Why?

If the length of an arc of a circle of radius r is equal to that of an arc of a circle of radius 2r, then the angle of the corresponding of the other circle. Is this statement false ? Why ?

If two equal chords of a circle in intersect within the circle,prove that: the segments of the chord are equal to the corresponding segments of the other chord.the line joining the point of intersection to the centre makes equal angles with the chords.

Prove that a diameter of a circle which bisects a chord of the circle also bisects the angle subtended by the chord at the centre of the circle.

If the perpendicular bisector of a chord AB of a circle PXAQBY intersects the circle at P and Q, prove that arc PXA cong"arc "PYB .

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.