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Perpendicular Bisector of Chord
Perpendicular Bisector of Chord
The perpendicular bisector of a chord will pass through the centre of the circle.
The perpendicular bisector of a chord will pass through the centre of the circle.
Conversely, when radius is perpendicular to a chord, the chord is bisected at the point of intersection.
Conversely, when radius is perpendicular to a chord, the chord is bisected at the point of intersection.
Explore!
Explore!
Use the applet below to explore the property of a Perpendicular Bisector of Chord.
Use the applet below to explore the property of a Perpendicular Bisector of Chord.
Move points A and B to shift the chord AB.
Move points A and B to shift the chord AB.
Click on 'Show Proof' to view 2 congruent triangles.
Click on 'Show Proof' to view 2 congruent triangles.
Proofs
Proofs
Given AM = BM, △OMB ≡ △OMA (By SSS Test) ∴ angle OMB = 90°.
Given AM = BM, △OMB ≡ △OMA (By SSS Test) ∴ angle OMB = 90°.
Given angle OMB = 90°, △OMB ≡ △OMA (By RHS Test) ∴ AM = BM.
Given angle OMB = 90°, △OMB ≡ △OMA (By RHS Test) ∴ AM = BM.
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