Question -
Answer -
Let mid-point of an arc AMB be M and TMTтАЩ be the tangent to the circle.
Join AB, AM and MB.
┬а
Since, arc AM = arc MB
=> Chord AM = Chord MB
In тИЖAMB, AM = MB
=> тИаMAB = тИаMBA тАжтАж(i)
[equal sides corresponding to the equal angle]
Since, TMTтАЩ is a tangent line.
тИаAMT = тИаMBA
[angle in alternate segment are equal]
тИаAMT = тИаMAB [from Eq. (i)]
But тИаAMT and тИаMAB are alternate angles, which is possible only when AB || TMTтАЩ
Hence, the tangent drawn at the mid-point of an arc of a circle is parallel to the chord joining the end points of the arc.
Hence proved