Construction Is A Piece Of Cake! Right? (Part-3)

Geometry Level 5

Mohit, influenced by Akshat and Anshuman, took a right ABC\bigtriangleup ABC (right angled at BB), where AB=5.5cmAB=5.5 \mathrm{ cm} and BC=8cmBC=8 \mathrm{ cm}, and started doing aimless constructions, the steps of which are given below:

(11) He drew perpendicular bisector X1Y1X_1Y_1 of ACAC which intersects ACAC at a point O,O, and another perpendicular bisector X2Y2X_2Y_2 of ABAB which intersects ABAB at a point GG.

(22) Then he constructed a circle taking center OO and radius of the circle as OAOA . Then he constructed an ACE\angle ACE which is equal to ACB\angle ACB such that EE lies on the circle.

(33) He then joined BEBE which meets ACAC at FF.

(44) Then he joined CGCG which intersects EBEB at HH and X1Y1X_1Y_1 at JJ.

Mohit then wondered what BHOJ\frac{BH}{OJ} could possibly be equal to.

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