PQ is a chord of a circle with centre O and PT is a tangent at P. A chord PQ is drawn and a chord each from P and Q are drawn namely PR and QR respectively such that point R is in the segment formed by PQ. Given that angle QPT= 700. Find angle PRQ .
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°