(i) ABC is a triangle with a right angle at A, and P is a point on the hypotenuse BC.
The line AP produced beyond P meets the line through B which is perpendicular to BC at U.
Prove that BU=BA if, and only if, CP=CA.
(ii) A is a point on the semicircle CB, and points X and Y are on the line segment BC.
The line AX, produced beyond X, meets the line through B which is perpendicular to BC at U.
Also the line AY, produced beyond Y, meets the line through C which is perpendicular to BC at V.
Given that BY=BA and CX=CA, determine the angle ∠VAU. geometryequal segmentsright trianglesemicircleangle