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 degree thenPAngle POA is equal to

Answer 1

angle PAO=90
angle PBO=90
THEREFORE ANGLE AOB+ANGLE APB=180
ANGLE POA = 50

Answer 2

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We know that tangent to a circle makes right angle with radius.

∴ ∠A = ∠B = 90° and ∠P = 80°

Sum of all angles of quadrilateral = 360°

∴ ∠A + ∠B + ∠P + ∠O = 360°

∴ 90° + 90° + 80° + ∠O = 360°

∠O = 100°

∠ AOP = ∠ BOP

∴ ∠POA = 50°