Prove thata the tangent drawn at the end of the chord of a circle make equal angles with the chord
Lost your password? Please enter your email address. You will receive a link and will create a new password via email.
Please briefly explain why you feel this question should be reported.
Please briefly explain why you feel this answer should be reported.
Please briefly explain why you feel this user should be reported.
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.