Question

38. In the figure below, points X and Y lie on the circle with

center O. CD and EF are tangent to the circle at X and Y.
respectively, and intersect at point Z. If the measure of XOY
is 60°, then what is the measure of CZF?
F. 45°
G. 60°
H 90°
J. 120°
K. 180°

Answer 1

Based on the information given, we can determine the measure of CZF by analyzing the angles in the figure.

Since CD and EF are tangent lines to the circle, the angles formed at X and Y between the tangents and radii are right angles. Therefore, angles OXC and OYF are both 90°.

Since the sum of angles in a triangle is 180°, we can find the measure of angle XOY:

XOY = 180° - OXC - OYF
XOY = 180° - 90° - 90°
XOY = 0°

However, this result contradicts the given information that the measure of XOY is 60°. Therefore, the information provided is not consistent, and we cannot determine the measure of CZF based on the given figure.