Prove that tangent drawn at the mid point of the are of a circle is pallelar to the chord joing the ends of point of the are

Explanation

GIVEN Point `P` is the midpoint of arc `hat(QR)` of a circle with centre `O`. `ST` is the tangent to the circle at point `P`.
TO PROVE Chord `QR||ST`.
PROOF `P` is the midpoint of `hat(QR)`
`implieshat(QP)=hat(PR)`
`implies` chord `QP=` chord `PR` [`:'` in a cirlce, if two arcs are equal, then their corresponding chords are equal]
`:./_PQR=/_PRQ`
`implies/_TPR=/_PRQ` [Note `/_PQR=/_TPR`, angles in alternate segments]
`impliesQR||ST` [`:' /_TPR` and `/_PRQ` are alternate int.]