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.

Explanation

Let AB and CD be the two equal chords i.e. AB = CD.

Let the chords intersect at point E and Join OE.

Draw perpendiculars from the center O to the chords and the Perpendicular bisects the chord AB at M and CD at N.

To prove: `angleOEN = angleOEM`

Proof : In `triangleOME` and `triangleONE`

`angleM=angleN=90^*` (each `90^*`)

`OE=OE` (common)

`OM=ON` (Equal chords are equidistant from the center)

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