Question

a tangent PA and PB from a point P to a circle with Centre O are inclined to each other at angle of 80 then what is the value of angle POA

Answer 1

tangents make 90 degree angle so according to cyclic quadrilateral the sum of four sides is 360 = 90+90+80 + poa
answer is 100 degree

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°