Question

In the figure, given below, O is the centre of the circumcircle of triangle XYZ.

Tangents at X and Y intersect at point T. Given ∠XTY = 80° and ∠XOZ = 140°, calculate the value of ∠ZXY.

Answer 1

In the figure, a circle with centre O, is the circumcircle of triangle XYZ.

∠XOZ = 140°  ...(Given)

Tangents at X and Y intersect at point T, such that ∠XTY = 80°

∴ ∠XOY = 180° – 80° = 100°

But, ∠XOY + ∠YOZ + ∠ZOX = 360°  ...[Angles at a point]

`=>` 100° + ∠YOZ + 140° = 360°

`=>` 240° + ∠YOZ = 360°

`=>` ∠YOZ = 360° – 240°

`=>` ∠YOZ = 120°

Now arc YZ subtends ∠YOZ at the centre and ∠YXZ at the remaining part of the circle.

∴ ∠YOZ = 2∠YXZ

`=> ∠YXZ = 1/2 ∠YOZ`

`=> ∠YXZ = 1/2 xx 120^circ = 60^circ`