PQ is a chord of a circle with centre O and PT is a tangent. If Angle QPT = 60, find Angle PRQ

PQ is a chord of a circle with centre O and PT is a tangent. If Angle

1.	PQ is a chord of a circle with centre O and PT is a tangent. If Angle QPT = 60, find Angle PRQ
Answer» Ans.\\(\\angle OPT = 90\\)\\(\\angle QPT = 60 \\space \\space \\space \\space(Given)\\)\\(\\angle OPQ = \\angle OPT - \\angle APT\\)\\(\\angle OPQ = 90-60 = 30 \\)\\(in \\triangle OPQ, OP = OQ\\)So,\\(\\angle OPQ = \\angle OQP = 30 \\)\\(\\angle POQ = 180-30-30 =120\\)\\(\\angle PLQ = 60 \\)PLQR is cyclic Quadrilateral, so\xa0\\(\\angle PRQ = 120 \\)\xa0