Question

In a circle with Centre O two tangents PA and PB are inclined each other at the angle 80° then ∠POA = ?​

Answer 1

In ∆POA and ∆POB

PA=PB

(Tengents from external point P)

OA=OB (Radius of circle)

and OP=OP

therefore, ∆POA=∆POB

(by SAS congruency)

= OPA = OPB

= OPA = OPB = 40°

Since the tengent at any point of a circle is perpendicular to the radius through the point of contact.

therefore, OAP = 90°

Now, in ∆OAP,

OAP + OPA + POA = 180°

= 90° + 40° + POA = 180°

= 130 + POA = 180°

= POA = 50°

Hence, the angle POA = 50°.