Question

If tangents PA and PB from a point P to a circle with centre 0 are inclined to each other at an angle of 80° .Find AOB
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Answer 1

Answer:

If tangents PA and PB from a point P to a circle with centre O are inclined to each other at angle of 80°, then ∠ POA is equal to. (A) 50° (B) 60° (C) 70° (D) 80°. Since, the tangent at any point of a circle is perpendicular to the radius through the point of contact.

Step-by-step explanation:

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Answer 2

50°

Step-by-step explanation:

See the diagram first.

Between ΔAOP and ΔBOP,  

(i) ∠OAP =∠OBP = 90° {Since tangent and line from origin meet at 90° to each other}

(ii) OA=OB= radius of the circle =r (Say)

and (iii) OP is the common side.

Hence, we can say ΔAOP ≅ ΔBOP

Therefore, we can say ∠OPA= ∠OPB =1/2(∠APB)=1/2(80°) =40°

{Since given that tangents PA and PB are inclined to each other by 80°}

Now, in ΔAOP, ∠POA +∠OPA +∠A =180°

⇒ ∠POA+40°+90°=180°

⇒ ∠POA=50° (Answer)