Question

Ch-circle
Q-ABCandADC are two triangle with common hypotenuse AC.prove that angel CAD =angelCBD
Q-prove that a cyclic parallelogram is a rectangle.

Answer 1

1) ang.CBD=ang.CAD ----------------theorem 10.9

2) let ABCD be a cyclic llgm 
in a llgm diagonals bisect;
so---DO=BO  and  AO=CO-------------------- 1
it is only possible when the diagonals are the diameters of the circle
now considering triangles DAB , ABC ,BCD and CDA
they all lies in the semi circle .i.e. angles  a,b,c and d are equal to 90.as they lie on semi circle
Now,its a llgm wuth all angles of 90 digree and hence a rect.