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THE DIAGNOLS OF A CYCLIC QUADRILATERAL ARE AT RIGHT ANGLES.PROVE THAT THE PERPENDICULAR FROM THE POINT OF INTERSECTION ON ANY SIDE WHEN PRODUCED BACKWARDS,BISECTS THE OPPOSITE SIDE.

Asked by vrishti TOKAS | 12th Jan, 2016, 12:49: PM

Expert Answer:

$begin mathsize 14px style angle E B O equals angle F C O space space space space space left parenthesis a n g l e s space i n space t h e space s a m e space s e g m e n t right parenthesis space space space.... left parenthesis 1 right parenthesis I n space r i g h t minus a n g l e d space t r i a n g l e space O F C comma angle O F C plus angle F C O plus angle C O F equals 180 90 degree plus angle F C O plus angle C O F equals 180 angle F C O plus angle C O F equals 90 space space space space space space..... left parenthesis 2 right parenthesis N o w comma space angle E O B plus angle B O C plus angle C O F equals 180 space space space space space left parenthesis E O F space i s space a space s t r a i g h t space l i n e right parenthesis angle E O B plus 90 plus angle C O F equals 180 angle E O B plus angle C O F equals 90 space space space space space space space space space.... left parenthesis 3 right parenthesis F r o m space left parenthesis 2 right parenthesis space a n d space left parenthesis 3 right parenthesis angle F C O plus angle C O F equals angle E O B plus angle C O F angle F C O equals angle E O B space space space space space space space space space.... left parenthesis 4 right parenthesis F r o m space left parenthesis 1 right parenthesis space a n d space left parenthesis 4 right parenthesis angle E B O equals angle E O B rightwards double arrow O E equals B E S i m i l a r l y comma space O E equals A E H e n c e comma space B E equals A E space...... space left parenthesis p r o v e d right parenthesis end style$

Answered by Rashmi Khot | 13th Jan, 2016, 11:51: AM

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