Question

please give me answer please ​

Answer 1

Take any point A on the circumcircle of the circle.

Join AP and AR.

∵ APQR is a cyclic quadrilateral.  

∴ ∠PAR + ∠PQR = 180°  [sum of opposite

 ∠PAR + 100° = 180°

⇒ ∠PAR = 80°

Since ∠POR and ∠PAR are the angles subtended by an arc PR at the centre of the circle and circumcircle of the circle .

∴ ∠POR = 2∠PAR = 2 × 80°  = 160°

∴ In △POR, we have OP = OR    [radii of same circle]

∠OPR = ∠ORP  [angles opposite to equal sides]

Now,∠POR +  ∠OPR + ∠ORP = 180°

⇒ 160° + ∠OPR + ∠OPR =  180°

⇒ 2∠OPR  = 20°

⇒ ∠OPR = 10°