Thereom of tangents that are equalornot

2
by nani321

2015-03-30T14:22:55+05:30
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
• Brainly User
2015-04-01T18:34:47+05:30
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