8.1.13

    13. OA and OB are two radii of a circle meeting at right angle. From A and B two parallel chords AX and BY are drawn. Prove AY⏊BX.

Given:   : OA and OB are two radii of a circle meeting at right angle. AX and BY are chords. 

To prove :  :AY ⏊ BX

Proof :    : Since  OA and OB are two radii of a circle meeting at right angle,

                  ∠AOB = 90•

                   ∠AXB =  ∠AYB =½  ∠AOB

                                             = 45• (The 1)

                    Since AX//BY, 

                     ∠XAZ =  ∠ZYB = 45  and 

                     ∠ AXZ =  ∠ YBZ = 45 

                     ∠ A =  ∠ X = 45•

                      ∠ A  + ∠ X = 90

                      ∴ ∠ AZX = 90

                     ∴   AY ⏊ BX