Prove thata the tangent drawn at the end of the chord of a circle make equal angles with the chord

Prove thata the tangent drawn at the end of the chord of a circle make

1.	Prove thata the tangent drawn at the end of the chord of a circle make equal angles with the chord
Answer» Yes , right answer Given:- A circle with center\xa0O,PA\xa0and\xa0PB\xa0are tangents drawn at ends\xa0A\xa0and\xa0B\xa0on chord\xa0AB.To prove:-\xa0∠PAB=∠PBAConstruction:- Join\xa0OA\xa0and\xa0OBProof:- In\xa0△AOB, we haveOA=OB(Radii\xa0of\xa0the\xa0same\xa0circle)∠OAB=∠OBA.....(1)(Angles\xa0opposite\xa0to\xa0equal\xa0sides)∠OAP=∠OBP=90(∵Radius⊥Tangent)⇒∠OAB+∠PAB=∠OBA+∠PBA⇒∠OAB+∠PAB=∠OAB+∠PBA(From\xa0(1))⇒∠PAB=∠PBAHence proved.