Question

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°

Answer 1

Answer:

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Answer 2

Answer:

justification

= In∆POA and ∆POB ( each of 90° )

= ∠PAO = ∠PBO (radii of the circle )

= OA = OB ( both the tangent )

= PA = PB ( CPCT )

= ∆ APO = ∠BPO

= ∠APO = 1 ∠APB = 1 × 80° = 40°

2 2

IN ∆PAO, ∠POA + ∠OAP = 180°

= 40° + ∠POA + 90° = 180°

= ∠POA = 50°