Question

An isosceles triangle PQR with PQ=PR in inscribed in circle C(O,r).If angle QOR=100°,find angle POQ and angle ROP.​

Answer 1

Answer:

In △PQR, we have

PQ = PR

⇒ ∠PQR = ∠PRQ

⇒ ∠PRQ = 35˚

∴ ∠QPR = 180˚ - (∠PQR + ∠PRQ)

= 180˚ - (35˚ + 35˚) = 110˚.

Since, PQTR is a cyclic quadrilateral.

∴ ∠P + ∠T = 180˚

⇒ ∠T = 180˚ – 110˚ = 70˚

In cyclic quadrilateral QSRT, we have

∠S + ∠T = 180˚

⇒ ∠S = 180˚ - 70˚ = 110˚