Question

thereom of tangents that are equalornot

Answer 1

STATEMENT :- The lengths of tangents drawn from an external point to a circle are equal.
Given:- A circle with center O,P is a point lying outside the circle and PA and PB are two tangents to the circle from P.
To prove :- PA = PB
Proof:-  join OA ,OB and OP
        <OAP = <OBP ------------------->(Angle between radii and tangents)
        In two right triangles 
          OA = OB  ------------------------->(radii of same circle)
          OP = OP  ------------------------->(common)
    Therefore, by R.H.S congruency axiom,
          ΔOAP ≡  ΔOBP
      ⇒PA = PB  -------------------------->(CPCT)
              HENCE PROVED

Answer 2

STATEMENT :- The lengths of tangents drawn from an external point to a circle are equal.
Given:- A circle with center O,P is a point lying outside the circle and PA and PB are two tangents to the circle from P.
To prove :- PA = PB
Proof:-  join OA ,OB and OP
        <OAP = <OBP ------------------->(Angle between radii and tangents)
        In two right triangles 
          OA = OB  ------------------------->(radii of same circle)
          OP = OP  ------------------------->(common)
    Therefore, by R.H.S congruency axiom,
          ΔOAP ≡  ΔOBP
      ⇒PA = PB  -------------------------->(CPCT)
              HENCE PROVED