(i)Side BC ofincrement A B C is produced to a point D.The bisector of angle A meets BC at L.Prove angle A B C plus angle A C D equals 2 angle A L C.
(ii)A point O is taken inside an equilateral four sided figure ABCD such that its distances from the angular points D & B are equal.Show that AO & OC are in one & the same straight line.

Asked by araima2001 | 13th Sep, 2014, 11:00: AM

Expert Answer:

In given equilateral four sided figure ABCD 

  AD = AB (becauseequilateral quadrilateral)

  AO = AO (becausecommon)

  OD = OB (becauseGiven)

Therefore , angle AOD = angle AOB  ……………..(1)

Similarly ,   angle CDO = angle BOC  ……………...(2)

But, angle AOD + angle AOB + angle CDO + angle BOC = 360

2 angle AOB + 2 angle BOC = 360  (From eqn (1) and (2) ) 

2 (angle AOB + angle BOC )= 360

 angle AOB + angle BOC = 180

 So, AO and OC are in same straight line 

Hence proved   

Answered by Dharma Teja | 14th Sep, 2014, 11:35: PM

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