Question

Angle X is a circumscribed angle of circle V.

Circle V is shown. Line segments Y V and W V are radii. Tangents Y X and W X intersect at point X outside of the circle. Angle X is a right angle.

Which name best describes figure VWXY?

square
parallelogram
quadrilateral
trapezoid

Answer 1

A

Explanation:

Answer 2

(A)Square

Explanation:

|YV|=|WV| (Radii of circle V)

|WX|=|YX| (Tangents to a Circle are equal)

`\angle VWX=\angle VYX=90^\circ ($Angle between a radius and a tangent)`

`Given: \angle WXY=90^\circ`

Using sum of angles in a quadrilateral,
`\angle WVY=90^\circ`

Since all the angles are 90 degrees, it means the length of opposite sides are equal.

Therefore:

|XY|=|YV|=|WV|=|WX| (all the four sides are equal).

The shape is a square since all the sides are equal and all the angles are 90 degrees.