Question

PQ is a chord of a circle with centre O and PT is tangent at P. If angle APT=60 degree. Then find angle PRQ where R is a point on the circle.

Answer 1

Answer:

Given : PQ is a chord of a circle with center O. Also, ∠QPT = 70°.

Now, ∠QPT + ∠QPX = 180° [Linear pair]

⇒ ∠QPX = 180° - ∠QPT = 180° - 70° = 110°

Again, ∠QPX = ∠PRQ [Alternate segment theorem]

⇒ ∠PRQ = 110°

Answer 2

Answer:

Given, PQ is a chord of a circle with center O. Also, ∠QPT = 60°. let x be the point on the tangent PT.

Now, ∠QPT + ∠QPX = 180° [Linear pair]

⇒ ∠QPX = 180° - ∠QPT = 180° - 60° = 120°

Again, ∠QPX = ∠PRQ [Alternate segment theorem]

⇒ ∠PRQ = 120°