Question

In the rectangle abcd, the perpendicular bisector of ac divides the longer side ab in a ratio 2: 1. then the angle between ac and bd is

Answer 1

HELLO DEAR,


If PQ is the perpendicular bisector of AC, intersecting AB at E and AC at 0, then 
AO = OC = AC/2
AE = 2EB = (2/3)AB

Triangles AOE and ABC are similar.
=> AO/AE = AB/AC
=> (AC/2)/{(2/3)AB} = AB/AC
=> AB = AC(rt3)/2

=> Angle CAB = 30
=> Angle between AC and BD is 60 or 120




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THANKS