Question

Prove that the line joining the mid points of two equal chords of a circle sub tends equal angle with the chord​

Answer 1

Answer:

Let AB and CD be the equal chords.

Let O be the centre of circle.

Let M and N be the mid-points of the chords.

Therefore,

MB=AM

CN=DN

Equal chords are equidistant from the centre.

∴OM=ON

Now in △OAB and △OCD

OA=OD(Radius of circle)

AB=CD(Given)

OB=OC(Radius of circle)

By SAS congruency,

△OAB≅△OCD

Now by C.P.C.T.,

∠AOB=∠COD

Hence proved that the line joining the mid-point of two equal chords of a circle subtends equal angles with the chord.