Question

in the given figure, EF is a line passing through the centre o of a circle. if EF bisect chord AB and CD of the circle prove that AB is parallel to CD.

Answer 1

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Answer 2

➡Given: In figure, EF is a line passing through the centre O of a circle. EF bisects chords AB and CD of the circle.

⭕To Prove: AB || CD.

Proof: ∵ EF bisects chord AB

∴ OL bisects chord AB

∴ ∠OLB = ∠OLA = 90° ...(1)

| ∵ The line drawn through the centre of a circle to bisect a chord is perpendicular to the chord

∵ EF bisects chord CD

∴ OM bisects chord CD

∴ ∠OMC = ∠OMD = 90° ...(2)

| ∵ The line drawn through the centre of a circle to bisect a chord is perpendicular to the chord

From (1) and (2),

∠OLB = ∠OMC = 90°

But these angles form a pair of equal alternate interior angles

∴ AB || CD.