Question

Given circle UU with radii start overline, U, V, end overline

UV
and start overline, U, W, end overline
UW
and chords start overline, X, W, end overline
XW
, start overline, X, V, end overline
XV
, start overline, Y, V, end overline
YV
and start overline, Y, W, end overline
YW
. Name an angle congruent to angle, V, Y, W∠VYW.

Answer 1

Since circle U has radii UV and UW and chords XW, XV, YV and YW, an angle that is congruent to ∠VYW is ∠XWY.

In Mathematics and Geometry, the theorem of intersecting chord states that when two chords intersect inside a circle, the measure of the angle formed by these chords is equal to one-half of the sum of the two (2) arcs it intercepts.

Additionally, the Congruent Inscribed Angles Theorem states that inscribed angles that intercept the same arc must be congruent.

Since homothety preserves the angles while multiplying the distances between points with its ratio, we can reasonably infer and logically deduce that the following angles are congruent;

∠VYW ≅ ∠XWY.

Complete Question:

Given circle U with radii UV and UW and chords XW, XV, YV and YW. Name an angle congruent to ∠VYW.