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

$\boxed{\textbf{QUESTION}}$
$<b>$
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

$\boxed{\textbf{Option (a)50°}}$

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Answer 2

Given :   tangents PA and PB from a point P to a circle with centre O, are inclined to each other at  an angle of 80°,

To Find : ∠POA

Solution:

PA & PB are tangent  and O is tangent

=> ∠OAP = ∠ OBP = 90°

PA and PB are inclined to each other at  80°

=> ∠APB = 80°

in Quadrilateral OAPB

∠AOB + ∠OAP  +  ∠APB + ∠ OBP = 360°

=> ∠APB + 90° + 80° + 90° = 360°

=>  ∠APB = 100°

∠POA = ∠POB = (1/2) ∠APB

=> ∠POA = (1/2) 100°

=> ∠POA = 50°

option a is correct

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