Question

in figure.o I'd the centre of circle of PQ is a chord and PT is tangent at P. which makes an angle of 50°with PQ,<poQ is--​

Answer 1

Answer:

We know, that radius is perpendicular to a tangent .

∴ ∠OPR=90°

⇒ ∠OPQ + ∠QPR=90°

⇒ ∠OPQ + 50° = 90°

⇒ ∠OPQ = 90° - 50°

⇒ ∠OPQ = 40°

⇒ OP=OQ [ Radii of a circle ]

⇒ ∠OPQ = ∠OQP = 40°. [Base angles of equal sides are also equal ]

In △POQ,

⇒ ∠OQP + ∠POQ + ∠OPQ = 180°

[Sum of angles of a triangle is 180°]

⇒ 40° + ∠POQ + 40° = 180°

⇒ ∠POQ + 80 = 180°

⇒ ∠POQ = 100°