Question

Circle C is shown. Secants U W and Y W intersect at point W outside of the circle. Secant U W intersect the circle at point V and secant Y W intersects the circle at point X.
In the diagram of circle C, m∠VWX is 43°. What is mArc V X?

39°
41°
78°
82°

Answer 1

82°

Reason: For two secants intersecting outside the circle, m∠ = 1/2(m arc (far–far) − m arc (near–near)). So
43 = 1/2(m arc UY − m arc VX) ⇒ m arc VX = m arc UY − 2·43.
From the diagram m arc UY = 168°, so m arc VX = 168 − 86 = 82°.