Question

12. If angle between tangents PA and PB of circle which have o as centre is 80 then POA =​

Answer 1

In triangle POA and triangle POB

PA = PB

(Tangents from external point P)

OA = OB (Radii of a circle)

and  OP = OP (common)

Hence, triangle POA ≅ POB

           (by SSS congruency)

⇒ angle OPA = angle OPB

⇒ angle OPA = angle OPB = 40 degree

Since, the tangents at any point of a circle is perpendicular to the radius through the point of contact

∴ angle OAP = 90 degree

Now, In triangle OAP,

angle OAP + angle OPA + angle POA = 180 degree

⇒ 90 + 40 + angle POA = 180 degree

⇒ 130 + angle POA = 180 degree

⇒ angle POA = 50 degree