Question

If two equal chords of a circle intersect within the circle, prove that the line joining the point of intersection to the center makes equal angle with the chords .​

Answer 1

In △OMX and △ONX,

∠OMX=∠ONX=90∘

OX=OX(common)

OM=ON where AB and CD are equal chords and equal chords are equidistant from the centre.

△OMX≅△ONX by RHS congruence rule.

∴∠OXM=∠OXN

i.e.,∠OXA=∠OXD

Hence proved.

Answer 2

Step-by-step explanation:

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If two equal chords of a circle intersect within the circle, prove that the line joining the point of intersection to the center makes equal angle with the chords .

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In △OMX and △ONX,

∠OMX=∠ONX=90∘

OX=OX(common)

OM=ON where AB and CD are equal chords and equal chords are equidistant from the centre.

△OMX≅△ONX by RHS congruence rule.

∴∠OXM=∠OXN

i.e.,∠OXA=∠OXD

Hence proved.