In the figure XY and XZ are tangents at points Y and Z respectively to a circle with centre O. If C is a point on the circle and ∠ZXY = 40°, then ∠ZCY = ?

1. 80°

2. 70°

3. 140°

4. 40°

From figure,

The tangent at any point of a circle and the radius through this point are perpendicular to each other.

∠OZX = 90°

∠OYX = 90°

∠ZXY + ∠ZOY + ∠OZX + ∠OYX = 360° [Angle sum property of quadrilateral]

40° + 90° + 90° + ∠ZOY = 360°

220° + ∠ZOY = 360°

∠ZOY = 360° - 220°

∠ZOY = 140°.

We know that,

Angle at the centre is double the angle at a point on the remaining part of the circle.

∠ZCY = $\dfrac{1}{2}$ ∠ZOY

∠ZCY = $\dfrac{140°}{2}$

∠ZCY = 70°.

Hence, option 2 is the correct option.