MathLabs

Problem 2

The angle at A A is the smallest angle in triangle ABC ABC . The points B,C B,C divide its circumcircle into two arcs. Let U U be an interior point of the arc BC BC not containing A A . The perpendicular bisectors of AB AB and AC AC meet line AU AU at V V and W W , respectively. The lines BV BV and CW CW meet at T T . Show that AU=TB+TC AU=TB+TC .
Step 4 of 4: Finish by lengths
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In plain words

Finish by lengths

AU=TB+TCAU=TB+TC
Detailed analysis

Now AU=CY=CT+TY=CT+TB AU=CY=CT+TY=CT+TB , proving the claim.