Question

In the alongside, figure, O is the centre of the circumcircle of triangle XYZ. Tangents at X and Y intersect at T. Given ∠XTY = 80° and ∠XOZ = 140°. Calculate the value of ∠ZXY.

Answer 1

∠ TXY = ∠ TYX = 50°           ...(since XT = YT)
∠ OXZ = ∠ OZX = 20°         ...(since OX = OZ)( In ΔXOZ, 140° + ∠ OXZ + ∠OZX = 180°)
⇒ ∠ OXZ = 20°
⇒ ∠ OXY = 40°                     ...(Since ∠OXT = 90°)
⇒ ∠ZXY = ∠ OXZ + ∠ OXY 
= 20° + 40° = 60°.